Banks offer a lot saving plans but still there is one thing that I am unable to understand that what is the purpose of saving by paying. Like banks will take their commission as well.

Commission? It is a form of investment. Banks pay you interest based on whatever rate they may use. I don't use banks for that, that is what Money Market accounts in Mutual Funds are for, IMO

You will never leave the bank with less money than you put in. I don't understand what you mean by commission. Commission for what? Banks actually pay you to put money in an account with them.