Dimension
Spatial dimensions
Classical physics theories describe three physical dimensions: from a particular point in space, the basic directions in which we can move are up/down, left/right, and forward/backward. Movement in any other direction can be expressed in terms of just these three. Moving down is the same as moving up a negative amount. Moving diagonally upward and forward is just as the name of the direction implies; i.e., moving in a linear combination of up and forward. In its simplest form: a line describes one dimension, a plane describes two dimensions, and a cube describes three dimensions.
Time
Time is often referred to as the "fourth dimension". It is, in essence, one way to measure physical change. It is perceived differently from the three spatial dimensions in that there is only one of it, and that movement seems to occur at a fixed rate and in one direction.
The equations used by physics to model reality often do not treat time in the same way that we as organisms perceive it. In particular, the equations of classical mechanics are symmetric with respect to time, and equations of quantum mechanics are typically symmetric if both time and other quantities (such as charge and parity) are reversed. In these models, the perception of time flowing in one direction is an artifact of the laws of thermodynamics (we perceive time as flowing in the direction of increasing entropy).
Together with the spatial dimensions, these dimensions form a four-dimensional manifold known as the space-time continuum.
Additional dimensions
Furthermore, theories such as string theory predict that the space we live in has in fact many more dimensions (frequently 10, 11 or 26), but that the universe measured along these additional dimensions is subatomic in size. As a result, we perceive only the three spatial dimensions that have macroscopic size.