There are two essentially different approaches one can take to time. One is to see time as a smooth continuum, so that even if one can talk about “instants” in time there are an infinite number of such instants, and when objects move they do so continuously, occupying all the points in space between their starting location and destination. The other possibility is to view time as a collection of snapshots. Between each of these snapshots there is nothing, but, like a movie, the snapshots are very close together, giving the illusion of continuous motion and events.
Clearly only one of these views can be correct. I would say at the moment that our understanding of physics is more easily reconciled with the view of time as a collection of snapshots. For example the notion of “quantum time”, specifically that there is some smallest possible interval of time, seems to support the “snapshots” view, since we can see the quantum unit of time as the “distance” between snapshots. It has been pointed out that integrals, often used in physics, presuppose the idea of a continuum that is integrated over. This is true, but we could also argue that integrals are simply an approximation of the real solution, and that they are only such a good approximation because the time slices are so close to each other.
A stronger objection to the “snapshots” view comes from a modified version of Zeno’s paradox concerning arrows in flight. Specifically, supporters of the continuum view of time argue that since each snapshot in the temporal sequence has effectively zero duration, a fact that I would accept, thus that it is clear no motion can occur during that instant, also an acceptable conclusion. However, if motion never occurs why do objects seem to move? The answer is to accept that motion, in the sense of continuous motion, is indeed an illusion. For example, if at time slice 1 the arrow is at point A and in time slice 2 it is at point B, and these time slices are sequential (there are no more slices between 1 and 2), then I would deny that the arrow has “moved” from point A to point B, in the sense that the arrow found in time slice 1 has somehow crossed the distance between A and B when we find it in time slice 2. I think all we can say is that we have an arrow at A in 1 and an arrow at B in 2. We might talk about them as if they are the same arrow, depending on how we define sameness, but if we really accept the “snapshots” interpretation of time we should also reject that somehow the arrow exists between the time slices, and thus there is no reason to say the arrow in 2 is connected to the arrow in 1. Essentially, the arrows are not the same because there is an important difference between them; they exist in different time slices. Thus, we would argue that those who think that this paradox defeats the “snapshots” interpretation are begging the question, by assuming that objects in subsequent time slices are one object that needs to move to be found at different locations in different time slices.
Of course the contents of the time slices are not arbitrary. If we accept the “snapshots” view we should view the snapshots as being connected by physical laws, since in a sense each time slice is “generated” by taking the previous slice and applying the physical laws to its contents, resulting in its contents. (Although it would be inconsistent to interpret this as meaning that the actual contents of the first slice are somehow manipulated, since at the very least there is no time outside the slices to manipulate them in.) One property of objects in a time slice is an instantaneous velocity vector. If an object in time slice 1 has an instantaneous velocity of 1 cm per quantum time unit due west then the subsequent time slice will contain an object exactly like the one found in time slice 1 except moved 1 cm to the west. This of course results in apparent motion, and so we can see that the “snapshots” view is not a denial of apparent motion, simply of continuous motion.
You can read a bit more about time (and causation) here.