Hi,
you have both possibilities,
If your animations are "in place", then you will have to implement the movement, mecanim will only trigger the animation and since it doesn't move, your character will go nowhere.
in most cases, the actual movement an direction will be handled separatly, that's likely always true for bipeds, but for exotic rigs, you may rely purely on animation own movement and orientation in space to have your character evolve around.
Does that make sense?
also, be aware that it's generally driven using physics, so you likely want to always animation in place, and then use the unity physics engine to move your character around to benefit from collisions etc etc.
bye,
Jean