A depository institution is a financial institution in the United States (such as a savings bank, commercial bank, savings and loan associations, or credit unions) that is legally allowed to accept monetary deposits from consumers. Federal depository institutions are regulated by the Federal Deposit Insurance Corporation (FDIC).
An example of a non-depository institution might be a mortgage bank. While licensed to lend, they cannot accept deposits.
Whereas formerly the Federal Reserve System controlled most of the credit system in the United States by its regulation of depository institutions, by 2014 depository institutions controlled no more than 20% of the credit market.
References
Depository institution Wikipedia(Text) CC BY-SA