We mentioned multisignature in the previous module in regards to pay to script hash, but just to explain again and elaborate on its potential uses, we generalize, saying that multisig enables what are called M-of-N transactions.
In simple terms, multisig is a way of cryptographically sharing a key between participants, and serves to distribute points of failure.
Imagine if you want to share a wallet with your family, or even with yourself.
For example, consider a 2-of-3 multisig.
Imagine I have a 2 of 3 multisig with my friends Derrick and Gloria.
Only two of us need to sign off on a transaction in order to send it.
But no one can just run off with our bitcoin since you need at least two of three keys.
And in this example, I have set up a two of three multisig with myself.
Instead of losing my private key and then subsequently losing all of my funds, I have more than one point of failure.
After losing one private key, i still have two of the three total keys, so I still have sufficient keys to access my funds in a 2-of-3 multisig scheme.
As another example, some exchanges and software wallet companies provide 2-of-3 or 3-of-5 multisig services.
In the 2-of-3 multisig case, you keep two of your keys, and a trusted third party such as the company holds the third.
The exchange can’t use your funds since they only have one key, but if you ever lose one of your keys, the company can step in and offer their key to help you recover your funds.
As you can imagine, this works similarly for 3-of-5 or any other M-of-N multisig.