AMMs use a mathematical formula (most commonly the constant product x·y=k) to quote prices for swaps. Traders don't match with other traders — they trade against the pool. This makes markets available 24/7 for any pair with liquidity, but also means price impact grows with trade size relative to pool depth. Different AMM designs (concentrated liquidity, stable pools, weighted pools) trade off capital efficiency against complexity.
Glossary
AMM
Automated Market Maker — a smart-contract pricing function that quotes prices from a liquidity pool.