Correspondent bank
A bank that holds an account relationship with another bank in order to process payments on its behalf in a currency or market where that bank has no presence.
Cross-border payments route through correspondents because most banks do not hold accounts with most other banks. A payment from Cairo to Milan may pass through two or three institutions that neither the payer nor the beneficiary chose and neither can see.
Each correspondent in the chain applies its own charges and runs its own compliance screening. The number of hops, rather than the size of any single fee, is what usually determines what a payment costs and how long it takes.