Peer to peer cryptocurrency exchange fulfills the gaps left by traditional cryptocurrency exchanges. Instead of matching trades according to the order book, P2P crypto exchanges match the people who make the orders directly. When the system finds a complementary match between a buyer and the seller, instead of facilitating the trade like traditional exchanges, it instead matches both the parties directly. This allows the buyer and the seller to set their own terms and conditions and come to an agreement.
The only point of intermediary between the seller and the buyer is when there is a dispute. This mediation is automated, and no human interaction is involved. It is a highly secure, private, decentralized way of conducting business.