Banks offer services such as checking and savings accounts. what do banks do with most of the money they receive in deposits from customers?

Banks lend this money to other customers, and they charge an interest on those loans, that will be the source of their profit. This is the main mechanism of the banking business models.

However, banks need to be cautious and keep a percentage of the deposits as liquid reserves  (sometimes they are even forced by law to limit to a certain %), in case those customers who have deposited their money in checking and saving accounts want to withdraw some.