Chromatography is a widely used laboratory technique of separating mixtures. Basically all types of chromatography have the same theory. There is a stationary phase and a mobile phase. The mobile phase is made to run over the stationary phase along with our given mixture. The separation of the given mixture into its constituent parts takes place because of the difference in the affinities of the mixture constituents towards the mobile as well as the stationary phase. This means that the mixture constituent that shows higher affinity towards the stationary phase travels slower inevitably (because it binds to the stationary phase on a chemical level and hence shows resistance towards the movement from it). And the mixture constituent that shows higher affinity towards the mobile phase (as compared to the stationary phase) travels faster for a larger distance along with it.
Thin Layer Chromatography (TLC) is the most common type of chromatographic technique as it is quite simple, fast and inexpensive. In TLC, a sheet of plastic, glass, etc. is coated with a thin layer of highly absorbent material (like silica gel, cellulose). This thin coating is our stationary phase. Now first, we load our mixture (to be separated) on to this stationary phase. Then we take a solvent (like water) and run it over this sheet (which has the stationary phase and mixture) and leave it undisturbed. This solvent moves over the sheet and is called the mobile phase. Again depending upon the constituent affinities on the mobile and stationary phase, the mixture constituents travel at different speeds and to different distances on the sheet and get separated.