I think the best description that can be had is that motion is representative of a fundamental process in physics that, as far as we know, does not admit further reduction into more elementary processes.

If one takes the reasonable understanding that an interaction is anything which causes a change in the physical state of an object, then given that part of the total physical state includes the object's position, changes in position must also be considered as the result of an interaction: we can say that every physical object always undergoes at least one self-interaction, and we can say this interaction converts the momentum of the particle, another part of its state, steadily into displacements. This is the interaction that generates motion, and it should be mentioned as such alongside other types of elementary interactions.

However, asking "what this is", beyond that, is not a question physics can answer, any more than it can answer what other types of interactions "are" beyond giving us descriptions of them, e.g. while we can talk of charged objects interacting with an electric field, say, only now to cause changes in their momentum, we cannot say what that interaction "is" any more than stating the fact of its existence and describing just how that it affects the charged object.

I think the best description that can be had is that motion is representative of a truly fundamental process in physics that, as far as we know, does not admit further reduction into more elementary processes.

If one takes the reasonable understanding that an interaction is anything which causes a change in the physical state of an object, then given that part of the total physical state includes the object's position, changes in position must also be considered as the result of such an interaction: we can say that every physical object always undergoes at least one self-interaction, which converts the momentum of the particle, another part of its state, steadily into displacements. This is the interaction that generates motion, and it should be mentioned as such alongside other types of elementary interactions.

However, asking "what this is", beyond that, is not a question physics can answer, any more than it can answer what the other types of interactions "are" beyond giving us descriptions of them, e.g. while we can talk of charged objects interacting with an electric field, say, only now to cause changes in their momentum, we cannot say what that interaction "is" any more than stating the fact of its existence and describing just how that it affects the charged object's physical state. Or to put it another way, we do not have access to the Universe's "source code", so to speak, so we don't get to see how anything is actually implemented "under the hood" :D

I think the best description that can be had is that motion is representative of a fundamental process in physics that, as far as we know, does not admit further reduction into more elementary processes. The motive process converts momentum into displacement at a steady rate, just as other processes may, likewise, alter momentum.

This is best accommodated within a more integrated framework for physics that sees a classical particle as having, at each time, a physical state described by

$$\mathrm{PS} := (P, \mathbf{p})$$

where $P$ is the particle's position in physical space, and $\mathbf{p}$ its momentum, and this state resides in what is called a phase space. The evolution of the particle's state is generated solely by the interactions it undergoes:

$$\frac{d\mathrm{PS}}{dt} = \text{sum of all 1-body interactions} + \text{sum of all 2-body interactions} + \cdots$$

Then motion is the outcome of the sole 1-body interaction which has the effect,

$$\frac{d\mathrm{PS}}{dt} = \left(\frac{\mathbf{p}}{m}, \mathbf{0}\right)$$

. This, of course, gives again, no reason as to why there is such an interaction, but it at least puts it on equal footing with other phenomena such as forces, which involve two or more bodies and cause changes in the momentum part of the state.

I think the best description that can be had is that motion is representative of a fundamental process in physics that, as far as we know, does not admit further reduction into more elementary processes.

If one takes the reasonable understanding that an interaction is anything which causes a change in the physical state of an object, then given that part of the total physical state includes the object's position, changes in position must also be considered as the result of an interaction: we can say that every physical object always undergoes at least one self-interaction, and we can say this interaction converts the momentum of the particle, another part of its state, steadily into displacements. This is the interaction that generates motion, and it should be mentioned as such alongside other types of elementary interactions.

However, asking "what this is", beyond that, is not a question physics can answer, any more than it can answer what other types of interactions "are" beyond giving us descriptions of them, e.g. while we can talk of charged objects interacting with an electric field, say, only now to cause changes in their momentum, we cannot say what that interaction "is" any more than stating the fact of its existence and describing just how that it affects the charged object.