Any other property you can imagine, let's say density for example, requires that the object have some size. Now let's examine what we mean when we say something is in motion. We are all familiar with motion. We see examples of motion all the time. All we need to do is to quantify this everyday experience a bit to apply it to mechanics.
Motion always implies the passage of time.
Let's define two specific times called early and late. If there is still a difference in position when time late is as close to time early as we can imagine, then we say the object is in motion. The other sense of that word, dimension, has to do with the nature of the space being considered. For our purposes, neglecting Einsteinian relativity, we live in a three dimensional space. The surface of a sheet of paper or a computer screen might represent a space of two dimensions.