The role of a middleman is covered in full under Intermediary, which explains how intermediaries work in banking, payments and markets and why they exist. This page gives a short definition and explains how the two words are used.
A middleman is any person or business that sits between a buyer and a seller, or between a sender and a receiver, and helps the deal happen. Examples include wholesalers between manufacturers and shops, brokers who match investors with markets, and banks that take deposits from savers and lend them to borrowers. In payments, card networks, processors and the intermediary banks used in international transfers all act as middlemen. They add value by providing trust, matching, credit or convenience, but they also add fees and delays, and each one is a point where data can be exposed or a payment can fail.
"Middleman" is the everyday and sometimes critical word, while "intermediary" is the neutral term used in finance and law. Crypto projects often promise to "cut out the middleman" through peer-to-peer networks and smart contracts, an idea economists call disintermediation. In practice, new intermediaries such as exchanges, custodians and wallet providers often take their place.