I have some difficulty understanding how we learn concepts and store in the brain. And what is the mechanism we use to categorize?

Concepts and categories are mainly learned from experience. There are some good models about this, but there is in fact very little work relating concepts and categories to the brain.

What we know from concepts and categories can be summarized in 2 current theories about it: one is that we learn from experience a prototype (i am sure you choose your name for that reason, right?), and this prototype is used also when we categorize new exemplars. The other theory says that we don't necessarily form a prototype from experience, but we store every exemplar of a category and then we use that information to categorize new exemplars of a category. There is quite a lot we understand about learning and categorizing, but also still a lot we don't know. People sometimes seem to use an "implicit model" when they are making categorizations and it is still not known how humans do that.