ERC20 is a pre-designed token with some implemented functions and seems that it would be useful for exchanging "digital assets". However, why the number of 20 has been considered as a part of its name? (why not for example, 30?) And also when exactly do we need to use ERC20 token contract? I mean what is exactly its use case?
ERC stands for Ethereum Request for Comment, and 20 is the number that was assigned to this request.
It was just the 20th Ethereum Request for Comment.
Your second question (what is ERC20's use case) is far too broad to be answered here, but these blog posts might help: