A correspondent is a financial institution, such as a bank or brokerage firm, that handles transactions on behalf of another financial institution that it can't complete on its own.
For example, if a US bank has a client who needs to make a payment to a supplier located overseas, the US bank would use its relationship with a correspondent bank in the supplier's home country to credit the supplier's bank account with money from its own client's account that had been transferred through an international payment system.