I've got many close friends, but there's an awful lot about friendship that is not demonstrative in my case.

This statement means that although the speaker has a lot of friends, they don’t often show how much they care about their friends. This could mean that they don’t tell their friends how much they mean to them, or give them a lot of physical hugs or affection. It could also mean that although the speaker has a lot of friendship, it’s not outwardly obvious because they don’t spend a lot of time together or talk about their emotions.