Multi Signature mostly known as MultiSig is a digital way of safeguard your fund/holdings (cryptocurrency) in a contract. Imagine, three people wanna start a business and for that reason they have stored all of their bitcoins to one address. All of them are holding the private key. As per their contract, they three are the owner of the funds but as all of them have the private key, anyone of them can transfer the bitcoin to his personal address.
In traditional banking system, Joint AND account is kind of MultiSig account. During my little researching, I found an interesting topic about MultiSig reflection in traditional system. A guy wanna create an account with his girlfriend where both party's signature will be required to withdraw money. Worth reading for better understanding the system-
https://www.reddit.com/r/personalfinance/comments/12hr45/is_it_possible_to_have_a_joint_savings_account/Go back to the previous story, three people with their bitcoin. Since anyone of them can move the fund without others permission, multisig wallet can be created where signatures from rest of the party will be required.
One example taken from
wikipedia-
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.
