What is the purpose of Component?

Scripting
1

When would I ever use Component and not MonoBehaviour?

2

You probably won’t.

Component is just the base class of MonoBehaviour.

It goes:
Object
Component
Behaviour
MonoBehaviour

It’s a slightly slimmed down version. Unity uses it internally for components that don’t need all the bells and whistles of MonoBehaviour. i.e. Invoke, Coroutines, and a few other things (just check out the documentation and see what MonoBehaviour adds on top of Component).