It is most useful to conceive of motion as a rate-of-change of position, so it presumes an established system of position. The philosophical question that then arises is whether there can be any absolute system of position that does not depend on the position of particular objects (or sets of objects) or whether a system of position must be only relative with respect to one or more existent objects. To put it another way, is it philosophically coherent to for the whole universe in toto to move?
Descartes took the view that the position of objects must be considered relative to other objects, and therefore motion was always relative to the position of other objects. He considered that when people would make statements of motion without explicit relational objects, this implicitly referred to motion relative to some contextual surrounding. In this sense, he believed that there was some natural or "true motion" relative to some natural/obvious surrounding context (though this is largely an epistemological issue rather than a metaphysical one in my view).
One way to assert an idea of "absolute motion" is to pick one or more arbitrary "fixed points" in space and measure position and direction relative to these (e.g., one could take four fixed points to establish a three-dimensional coordinate system). The difficulty of this approach is that it relies on alleged "fixed points" that are not themselves moveable objects in space (for if they were objects that could move themselves then you would be back to a relative position system). The difficulty with this approach is that such points are inherently unobservable, so the "absolute motion" of objects then becomes unobservable. Leibniz famously critiqued this "absolute motion" approach, saying that since absolute velocity would be unobservable, it is really just made-up.