What does giving a item to someone mean?

So, I keep seeing characters in j-dramas, manga, anime, books, etc, giving personal items to another character when they're leaving or for good luck or something - and I just want someone to clarify me on what it exactly mean.

Does it mean 'You're very special to me, and I'll come back to you for it' or 'As my friend, you'll need to have this for luck' or something else? I'm scratching my head here, and all I can think of if people in Japan actually do this? Has? Still?

Yes, it's common to send a small gift of farewell when someone is leaving for a long journey or leaving for good. Like any other gifts, I suppose it shows the sender's thoughtfulness and will give the reciever something to remember about which would make the sender happy too. Of course, depending on the situation, one might wish good luck or attach some extra friendship or romatic feelings while (s)he's at it.

Wasn't the question about giving a personal item, not a small bought gift? Is "senbetsu" a bought gift or a personal item that is meant to be returned someday?

A senbetsu can either be a bought gift or a personal item, just like any gift can be. But I didn't understand the part where the poster asks "that is meant to be returned someday".

Uco, what I meant for "I'm going to get it back" is if people, well, want to get it back. Or something. Anyway, that question is just an example for my question because I didn't know what senbetsu is. Thanks guys!