My girlfriend got me started on watching Better Call Saul, and one thing I think that show does so well is use "character giving" to show multiple things:
It tells what a character's capabilities are. A character who gives someone a new car without having to change their lifestyle and a character who has to work tirelessly for a used bicycle are very different when it comes to how they do things, and the gifts they give show what has value to them and what doesn't.
It establishes relationships. If you know what has the most value to a character, you know what it means when that character gives it to someone else. A character swamped with work giving 10 minutes just to listen and help someone shows a strong bond between those two. If the character sits on a beach all day but refuses to give 2 minutes to a co-worker, you know there is no close feeling between them. This can be done to show rather than tell about character relationships, and avoid cheesy dialogue like "we've been friends since kindergarten" or "you don't like me and I get that."
It gives insight about the receiver. A character receiving something from another character can refuse it or change it, and it shows what motivates them and where their insecurities lie. If they get a better job offer but turn it down because they feel indebted to their current employer, you know they feel trapped. If they are offered a photograph of someone and they frame it and put it on their desk, it shows they want that person in their life.
It shows character and moral conflicts. A gift can have significance to the character giving or receiving it, and if that gift is refused, you know there's tension between them. Gifts can also establish plot, and drive conflict. If a character is given $10,000 of stolen money, and they find out it's stolen, it puts them in a situation where they have to make a moral choice. If they are given a precious memento, and they lose it, it can have serious consequences on their behaviour going forward. Just something I noticed that I never thought about before and wanted to share.
Tl;dr- the things your characters give each other can be used to show character capabilities, values, relationships, motivations, and establish conflict or even drive the plot. It's a great tool to use between characters to show rather than tell your audience more about them when done well.