"Claiming" means telling someone that something belongs to you. It's like saying "This toy is mine!" or "I found this book first!"
After claiming something, you need to do something to prove that it's really yours. This could mean showing a receipt or a piece of paper that says you bought it, or giving an explanation of how you came to possess it.
If other people also think the thing belongs to them, you might need to talk it out or get help from someone in charge (like a teacher or a parent) to decide who it really belongs to.
Once it's been decided that you are the rightful owner, you can use or keep the thing however you like (as long as it's legal and safe, of course!).