Multi-signature wallets are covered in full under Multi-Sig Wallet, which explains how they are set up, who uses them and their risks. This page explains the underlying technique and its name.
Multi-signature, shortened to multi-sig, is a rule that a transaction is valid only if it carries approvals from several different private keys, out of a defined group. The rule is described as "m of n": a 2-of-3 arrangement has three keys, any two of which must sign. Each approval is an ordinary digital signature; what makes it multi-sig is that the network or a smart contract refuses to move funds until enough of them are present.
On Bitcoin, multi-sig is built into the scripting system and became practical with a 2012 upgrade that let such conditions be hidden behind an ordinary-looking address. On Ethereum, it is usually provided by smart-contract wallets. The approach protects against the loss or theft of a single key and enforces shared control, which is why companies, funds and DAOs use it for treasuries.
A related technique, multi-party computation, achieves similar shared control by splitting one key into pieces, producing a single signature rather than several visible on-chain.