Chromatography is based on the difference in rates of adsorption of different substances on the surface of a suitable adsorbent.
Let's put that in simple words. Some stuff sticks better than other stuff. If the stuff sticks better, it would move slowly. That's the basic idea. Just like boiling points are different, this ability called adsorption is also different for different stuff.
We try to use this fact to separate substances in a mixture. So we went and found some special solvents which would help us do this. If we add a mixture to this solvent, some stuff would move faster and some slower. This would make them separate, just like we wanted!
Here's a small illustration.