Artifacts, mementos, keepsakes and other personal items mark off the series and its characters and represent various things to the characters and the readers. Very often, these mark off different parts of the story and create memorability for these situations.
In various time-frames of the series (though the series only refers as far as a decade before Lucy's escape), items of clothing come to be important.
A gift to young Lucy from Kouta, the ski cap has several meanings in the series. The ski cap Lucy wears is, in fact, a key plot device. In addition to giving Lucy the physical ability to blend in for the first time, it represents her character's mental ability to co-exist with Humans and live a regular life. Lucy is shown playing with Kouta and being an ordinary little girl while she is wearing the cap, but takes it off right before she starts the carnival massacre. After killing Kouta's family, Lucy keeps the cap as a memento of her time with Kouta and a reminder of her desire to one day meet him again and apologize for her misdeeds. In the anime, Lucy shares her treasured cap with her second friend Aiko, then in both versions loses her friend and memento at the same time. It is after removing the cap that Lucy becomes the more cruel person from the start of the series. After that point, her rebirth as Nyu becomes her best hope of living peacefully.
As Nyu, she sometimes wears a twin-tailed jester-looking cap, bought for her by Yuka. Whether intentional on Yuka's part or not, the hat serves two purposes. The first and most obvious one is to hide Nyu's horns, not only from direct view but also from sighting by shape, which a smaller more form-fitting cap might do by accident, while also being broad enough to slip on her quickly in case of visitors to Maple House who is unaware of the horns. A secondary purpose may be the obvious silliness and childishness of the cap and the attendant outfit, making Nyu's odd behavior easier to dismiss for some.
Before setting off on her mission to capture Lucy, Nana asked Kurama for his necktie, which he, of course, gave to her. Other than the dress given to her for that mission, it was the first piece of real clothing she had ever received. She was only allowed to have the dress so she could carry out her mission without drawing extra attention to herself. This distinction means that the tie was the first item of clothing given her as a gift. Why would clothing be particularly important to Nana? The Diclonius were kept naked at the Diclonius Research Institute to dehumanize them. Historically, some scientists in the service of brutal regimes can justify to themselves performing sometimes horrendous experiments by considering their subjects sub-human. In World War Two, Japanese Unit 731 and Nazis like Doctor Josef Mengele denied clothing to their test subjects for this reason. By freely giving her a tie, Kurama was recognizing Nana's humanity and showing that he didn't feel all Diclonius were simply monsters. Nana regarded the tie as a keepsake of her beloved father figure, even though she wore it incorrectly. When she lay in a bloody mess after her costly battle with Lucy, Nana apologized for staining the tie with her blood. A figure of Nana wearing the necktie/headband is a rare collectible.
It is unknown if this served as an inspiration for Lynn Okamoto, but in the Harry Potter novels, Harry frees the enslaved House Elf Dobby by tricking his abusive master, Lucius Malfoy, into giving him a sock, clothing signifying freedom in this instance. Later efforts to free all House Elves by Hermione Granger by giving clothes incurred resentment from the Elves of Hogwarts' staff, which while it can indicate Stockholm Syndrome, in this case, showed that the situation was more complicated than Hermione had banked on. No such complication exists for most Diclonius, who seek to escape at any chance they get, no matter the risk.
While at least one character describes her as looking disheveled, in fact, Mayu seemed to give off an appearance of near-normalcy while homeless. She wore a sweater-looking top meant to go with a skirt, said skirt abandoned when she fled her stepfather's final attempt to rape her once again. The series never says for certain whether she manages to go completely unnoticed in this state of dress/undress or whether people did not wish to take responsibility for her simply ignore her. It seems a combination of both, but the sweater-top is of note if only by its service to the plot. It is not frayed or dirty, to appearances - neither Kouta nor the particular Yuka comment on what the girl is wearing, when they first meet her. It seems almost long enough to cover her panties. Somehow, Mayu, during her time on the streets, appears to have found a way to keep it, herself and Wanta clean enough to not draw notice, even living on a beach while sleeping on sand. This condition may or may not point to Mayu's time on the streets being weeks rather than months, along with the thought that she seemed to have no alternative plans when her methods of survival closed down one by one. The garment seems sturdy, however much time Mayu spent as homeless, and she is seen wearing it at least once more in the series, with perhaps the hard memories associated with it replaced by it being the clothes she wore when she moved into Maple House.
Kouta's Batman Shirt
In Episode 5 of the anime, Kouta is seen by the house dining table wearing a T-Shirt with the Yellow Bat-Shield of the iconic superhero, or at least part of it seen through the overshirt he's wearing. While it could simply be something a young man in any country could and would wear, and while it may simply be a nod by one of the creative staff who's a Bat-Fan, there is something else to consider. It could be seen as Kouta's memories fighting to resurface, since he and Bruce Wayne both lost their families to violence, and had their lives' directions transformed by it, although obviously in radically different directions.
Kouta's Number 9 Shirt and Nana's Pac-Man windbreaker
In Episode 11 of the anime, Kouta is seen wearing a shirt with a circled Number 9 in stylized writing. It could mean anything, from the number of a favored athlete to simply a Number 9 with no further meaning. One possibility is that this Number 9 represents the Shooting Star, the race car used in Mach Go Go Go/Speed Racer by Fekumen Resa/Racer X, aka Mifune Kenichi/Rex Racer, the older brother and protector of the series' protagonist, Mifune Go/Speed Racer. Since the Masked Racer is an older brother who acted successfully to aid and protect his younger sibling, Kouta, who feels he failed at this with Kanae (in fact, he expresses his regrets over her while wearing this very shirt), may wear it to feel worthy of protecting those he has now.
In this same episode, Nana is given new clothes to wear after she establishes herself at Maple House, and among these things is a light jacket/windbreaker with a small emblem of the video game character Pakkuman/Pac-Man on the chest. This jacket is among the clothes shredded when Nana faces Mariko at Enoshima. Perhaps it simply has no meaning beyond this, but just as Pac-Man has always to keep going and keep ahead of those who wish him harm, so it is for the plucky Nana. Or it could just imply that the relationship between Mayu and Nana is so intimate that they share the Pac-Man shirt or the clothes were handed down from Mayu to Nana by Yuka's decision. Another scene that shows that they have a decent life to save living expenses.
The music box appears only in the anime and is a significant artifact for both Kouta and Lucy. The music box plays the beautiful, but sad melody called Lilium, which also serves as the opening theme of the series. Kouta has the music box when he first meets Lucy, and their first conversation is about how they both love the song. The music box is vital to Lucy because it reminds her of Kouta. At the end of the series, the music box stops playing, which probably represents the death of her Lucy personality. At that same time, the grandfather clock that Nyuu liked starts chiming, which represents the beginning of her life as Nyuu and shows the completion of rebirth. Lucy stated that she wished to start over again, and somehow be with her beloved Kouta. To do that and purge herself of the sadism and hatred that had built up inside her through years of discrimination and abuse, Lucy needed a sort of rebirth. Lucy continued living until she could apologize to Kouta, and after one final act of redemption by facing Kakuzawa's army and possibly saving the world by screwing up his plans (which require her body or at least head) the Lucy part of her personality was finally able to rest in peace.
Like the music box, the grandfather clock appears only in the anime series. Nyuu takes an interest in the broken clock and develops an obsession with fixing it. This focus possibly represents her desire to fix her broken life and her broken relationship with Kouta. The clock seems to represent Nyuu in the final scene since she was the character most associated with the clock. The clock suddenly coming back to life when the music box stops to indicate the beginning of her new life as Nyuu, as mentioned in the paragraph above. It is likely that this Nyuu wouldn't be the childish Nyuu from the start of the series, but a more mature version similar to Lucy but sans the violent tendencies. In fact, a more mature Nyuu does appear in the latter part of the manga. It also makes sense considering Nyuu's rapid psychological development in the few weeks the anime takes place. It is still debated within the fandom what the clock represents, but it is one of the more significant uses of symbolism in the series.
Carnival Carving Games
Before his traumas, Kouta was quite good at carving games, a game of skill in which one must use a hobby knife style cutter to carve shapes out of a block without breaking it. Harder than it sounds, prizes are awarded based on the difficulty grade of the puzzle and its ornateness. Yuka chafed at the fact that she was not good at even the simplest of these, and vowed to become better than Kouta when next she saw him. Sadly, she had eight years to practice this, which she did despite having no direct evidence that Kouta, traumatized by his family's murders, is ever coming back to Kamakura. Just after the start of the series, just before she fully realizes that Kouta's trauma has given him amnesia, Yuka smashes all the completed games she has saved up over the years, despairing of ever achieving her childhood goals. It is this frustration that in turn leads her to move into Maple House, and quickly realize that Kouta is not merely insensitive or forgetful.
Kouta gives the young Lucy a jade stone he finds in a stream. It immediately becomes a treasure to her, and, along with the ski cap, may well be the first gift the alienated girl has ever received. It sadly becomes part of the narrative that breaks young Lucy's heart when she believes Kouta has betrayed her. How deeply this gift affects her comes through in the fact that this plus a note confessing her love--as well as her actual name, inexplicably never asked for by Kouta--are buried in a glass jar next to where she laid her beloved puppy to rest. That stark declaration of love that went so very wrong kept preserved is part and parcel of the heart-raising moments that bring a very dark series to an actual happy ending.
Notes Of Note
On a few occasions, characters reveal part of their character by what they say when they are not there.
Mayu wrote a heartfelt note of thanks for the first kind acts of Kouta and Yuka before she finally moved into Maple House.
Kurama left a note with Nana, after he sent her away from the Institute, to spare her from Chief Kakuzawa's execution order. The anime renders this a recording, likely a nod to the fact that Nana did not know how to read.
Finally, and most importantly, the late Lucy was shown to have buried a message in a bottle, near her puppy's grave. It revealed her real name and feelings to Kouta, giving him an insight into his long-ago friend just before the series' very final twist.