The "enable" password is sort of like the root account on Cisco gear. When you first connect, you're in a low-priv state where you can do simple things like see the uptime of the device, interface info, etc. But to make any changes to the settings on the router, you have to run the "enable" command which typically asks for a password which is separate from the login password.

I guess the name comes from enabling admin functionality, but I don't know why Cisco didn't call the command admin. Anyway, this enable is different from enabling/disabling the login authentication.