Matt's Important Item: Harmonica
No surprise here but this is what inspired me to actually write these. Well, this and Tai's telescope.
Matt brings a harmonica. Unlike most of the others, who brought an item they thought they would need for camp, Matt likely always has his harmonica on him, at least until he moves on to a bass guitar.
When the others are sharing what they brought, Matt simply says he doesn't have any food. We don't see him with his harmonica until the next episode, when he runs off after Tai accidentally says something insensitive, to play the harmonica away from the others.
Matt's harmonica is a Blues Harp in the key of D. Most beginners start with a harmonica in C. As we see him playing this same harmonica in TK's flashback at Primary Village, we can assume Matt just always played on a D harmonica.
The harmonica is an iconic part of American blues music. It can also be played alone, and thematically it's used to express loneliness and solitude. A character playing the harmonica by themselves is almost always seen as melancholy.
Matt has this item purely for his own satisfaction; any time he's feeling too much, he plays the harmonica to cope. Or he'll just play it when he's bored, a good way to keep others from striking up conversation. In any case, while he might have originally brought it with him to camp to keep himself occupied without having to socialize, eventually he starts playing it for the benefit of others. At least once he plays it while the kids are fishing, filling the silence. I imagine that having music to listen to would calm some frazzled nerves.
For the most part, though, Matt's harmonica is linked to the side of himself he doesn't often show. Joe gives it back to him after the Dark Cave incident; we can assume that Matt ditched it due to his depression. When he gets it back, it's like he's whole again.
It's pretty significant that, when Matt and Gabumon are saying goodbye at the end of the season, they don't say much to each other. Instead, after sitting in silence for awhile, Matt plays the harmonica for Gabumon. Matt can put all his feelings into the songs he plays, especially when talking about those feelings is hard for him.