Then when the entity is being drawn, the number from the entity's state can represent which row in the texture to loop through for animation, so if it is resting the 1st row of frames are used, if it is walking the 2nd are used and so on.
I have little experience in anything other than games I'm afraid but that's how I use them.
Enumerations are mainly used for states (like in the example given above). They are special in the way that they have a "built-in check", since only defined values are accepted. You should normally not have to use them, but whenever you should, do it.