Multisignature (multi-signature) is a digital signature scheme which allows a group of users to sign a single document. Usually, a multisignature algorithm produces a joint signature that is more compact than a collection of distinct signatures from all users.
Multisignature can be considered as generalization of both group and ring signatures.
Multisignature in cryptocurrencies
Multisignature (often called multisig) is a form of technology used to add additional security and for bitcoin transactions. Multisignature addresses require another user or users sign a transaction before it can be broadcast onto the block chain. The required number of signatures is agreed at the start once people agree to create the address.
The first multisignature wallet was launched in August 2013 by BitGo.
Multisignature allows the creation of 2-of-3 escrow services. For example: when Alice wants to pay Bob, she sends a transaction to a multisignature address, which requires at least two signatures from the group "Alice, Bob and Trent" to redeem the money. If Alice and Bob disagree on who should get the money (Alice wants a refund, whilst Bob believes he fulfilled his obligations and demands the payment), they can appeal to Trent. Trent grants his signature to Alice or Bob, so one of them can redeem the funds.
Despite the name, multisignature in bitcoin is just a tuple of distinct user's signatures, not a single entity.
Multisignature scheme is also implemented in other non-bitcoin-based cryptocurrencies. Usually it replicates the same functionality via several distinct signatures.