Random motion is unpredictable according to current theory. We now know that atoms move. For example, an atom in a gas is free to bounce around within its container. This motion appears random, but is completely predictable according to current theories of classical mechanics . In practice, however, there is no way to do this with any degree of accuracy for an extended period of time.
Every measurement has error associated with it.
Now imagine that you were trying to predict the motion of a billion gas atoms in a container. After measuring the position and velocity of each one as accurately as possible, you enter the data in a monstrous computer and let it do the calculations for you. Since the measurements associated with each atom are a little off, the first round of computation will be a little wrong. Those wrong numbers will then be used in the next round of calculation and the results will be a little more wrong. After a billion calculations, the compounded error would render the results useless.