Use Sparrow or Liana wallet and you will understand it better.

Its actually pretty simple to think about.

1 of 3 (just an example. One of the 3 keys available needs to sign)
2-of-5 (2 of the 5 keys that exist need to sign)

Multi-signature flow uses PSBT files a lot. You may be familiar with PSBT files if you use an airgapped signing device (as opposed to a USB or bluetooth signing device).

When the PSBT file is signed with one of the available signatures, you take the partially signed bitcoin transaction file (PSBT file) and send it to the next person to sign.

Multi-signature requires multiple signatures, not multiple peopleMulti-signature requires multiple signatures, not multiple people

Multi-signature as 2FAMulti-signature as 2FA

So in this way, you can think of it like 2FA (two factor authentication). One device signs, but you need another device to sign. The most simplistic example of this, is the bitkey. The Bitkey is an airgapped signing device, but the wallet people make with the bitkey is NOT cold storage. This is because 2 of the 3 available keys are required to sign. 1 key is in the app (on the phone), one key is with the company, and the 3rd key is on the signing device. So in this way, the bitkey is a 2FA solution, not a cold storage solution.

Multi-signature as hardened securityMulti-signature as hardened security

On the other end of the spectrum is geographically distributed key storage. In this set-up, physical access to multiple locations is required to spend the life savings or whatever it may be. Glacier protocol guide explains the reason someone may want to do this:

https://glacierprotocol.org/docs/overview/multi-signature-security/

Multisignature security protects against the following scenarios:

Theft: Even if somebody physically breaks into a safe, any one key is not enough to steal the money.
Loss: If a key is destroyed or simply misplaced, you can recover your money using the remaining keys.
Betrayal: You may want to entrust one or more signatories with keys to facilitate access to your funds when you are dead or incapacitated. With multisignature security, entrusting them with a key will not enable them to steal your funds (unless they steal additional key(s), or collude with another signatory).

Multi-signature as collaborative custodyMulti-signature as collaborative custody

It may be the case that you don't want to be the sole custodian for your own funds. There are many reasons for this. A company or nation state for example should not have 1 person who can make spending decisions. Very often collaborative custody is used as a hand holding option to get people to learn self-custody, while still in reality having a custodian (bitcoin beach wallet when it existed was this kind of training wheels). Anchorwatch wants people to use this kind of multi-signature scheme for "self-custody insurance" From my understanding though anchorwatch will allow many different types of multi-signature arrangements including collaborate custody and multi-signature as inheritance (I'll allow them to explain themselves more, but point is don't get too caught up in that example).

One could also use this kind of collaborative custody the way one would use a joint bank account. For spouses, for event savings (like saving up for a family gathering in which the family collaboratively custodies the funds) Theya wallet is probably the most user friendly software that would allow for this usecase: https://www.theya.us/

The glacier protocol suggests a version of collaborative custody (given the user accepts the risk trade offs) wherein the user can spend at all times, but multiple friends or family members must collude to spend.

Multi-signature as inheritanceMulti-signature as inheritance

For this kind of multi-signature, even a 1-of-2 is reasonable. But why have a 1 of 2 instead of just sharing one key? Because in this setup, the key that the inheritance recipient holds, can not be used until a specified amount of time has passed.

Liana wallet is the user friendly program for setting something like this up:
https://wizardsardine.com/liana/

Key exchangeKey exchange

To create a multi-sig wallet with other people, you do not need to see each others private keys or seed phrases. You only need to share each others xpubs (and use the same derivation paths). This information is used to view the wallet balance, while the private key or seed phrase is used to sign.

Hope this helps.