As an example, for a 3d character. "Static" would be something like a running animation. Overwrite would be something like a melee (so you can run and hit something at the same time). Additive would be aiming, the rotation of the head and arms to modify depending on where you are aiming.
So now there are some conflict as when a melee animation is happening, then there shouldn't be any aiming, otherwise it would distort the melee animation.
I know i've read about state machines but i can't wrap my head around some ideas. ...
Look for the keywords
* animation blending: mixing animations on the same parts using weights,
* animation layering: overriding animations or suppressing them,
* animation masking: applying an animation only to the parts that are marked (e.g. specific body parts of a skeleton).
A state machine is useful to select animations, but its isn't useful for the mentioned purposes. The construct to control above mechanisms is often called animation tree or blend tree.