Newton, following on Descartes, defines motion as the transference of a body from one region of absolute space to another. Aristotelians point out that the definition is straightforwardly circular since transference is clearly a sort of motion. So it seems all that Newton, Descartes, and the mechanical tradition are saying is that motion is a sort of motion, which hardly does much to give one confidence in the philosophical value of mechanism. Some attempts have been made to justify definitions like this by claiming that it is impossible to define fundamental realities. But that line of argumentation is of no value in this case since to give a definition of motion is incompatible with believing it is undefinable.
A better account of what Newton is doing here is that he is attempting to give a definition in the sense articulating what one must know per se and primo in order to derive all the properties of the thing one wants to understand. Motion is to be seen as first of all taking place in the theater of absolute space, that is, the fundamental thing that one must know about motion is that it plays itself out against a homogeneous, immobile, quantitative backdrop. We come to understand this backdrop, as we understand all things, by distinguishing it, and to distinguish the homogeneous and quantitative gives rise to number. Absolute space is what is most formal to the definition, which is why Newton was led to make absolute space play the role of the specific difference in the definition.
That the definition was an attempt to make space the fundamental reality from which nature is to be explained also seems to follow from the controversies over space in Newton’s own day. Newton had to explicitly separate space from God himself in response to Berkeley’s critique that he identified the two. There is something divine about space, to be sure, as that within which all things live and move and have their being. It’s this vision of what is most divine and fundamental that serves as the basis of mathematical/mechanist philosophy, even to this day.