A dimension pretty much means the minimum number of coordinates needed to specify a point within the space of that dimension, and dimensions can't exist alone without including the lower dimensions, if so it's just another 1D space, nothing special.
But dimensions are interesting because we can't prove it, and the reason we can't prove it is because [[Science Doesn't Prove Anything]].
Spacetime is a [[4 dimension]]al manifold that fuses our 3-dimensional space world and time. In research string theories offer many more dimensions than the four ones, but they are still at the research level and no standard model exists. No new predictions to be validated or lead to falsifications have been proposed. If/when research reaches this point and the data validate string predictions then we can talk of the existence of higher dimensions than four in our model of physical reality.