Why does knowing accounts help a lawyer deal better with his clients ?

What kind of accounts? If you're talking about files lawyers keep themselves on clients, then it's to make sure that they have all the information. When it comes to legal issues, proof of anything is the point even if it seems tiny and insignificant.

If you're talking about a bank account, then again it comes with the proof thing. Usually though they would either request it from you to get it or with special requesting documentation.