The authorized_keys file is composed of the public keys for users who are permitted remote access to that account on that system.
In general, you have a set of keys for each user account, on each system. The private key is kept only on the system where it was created, and the public key is copied to other systems. In the case of SSH, the public key is copied into the authorized_keys file for your account on a remote system. Using keys can be both more convenient and more secure than relying on passwords for SSH access.
Imagine you're setting up a remote server, that you and several other people will operate, though a shared account on that server. You copy the public key from your local system, and the public keys from the other people, into the authorized_keys file for that remote system. This will allow all of you to access that remote server through keys as soon as it's set up. If you were setting up a lot of identical servers, you could simply copy the same authorized_keys file to each of them. If someone leaves the team, you can simply remove their public key from the authorized_keys file, and they should no longer have access to that system.
Here's some more general information on SSH: