Computer models of the atmosphere are approximations. We know the actual laws of motion for the atmosphere exactly; these are known as the Navier-Stokes equations. However, these equations have a property known as non-linearity; they can not be solved for exactly because the variables within them change in time and depend on each other. Therefore, we have to approximate.
So basically, we use computers to guess the weather by the patterns they're showing, these only work best about a couple hours before hand.
