The separation of compounds is due to the differences in their attraction to the stationary phase and because of differences in solubility in the solvent. As a result, the compounds and the mobile phase compete for binding sites on the stationary phase. Different compounds in the sample mixture travel at different rates due to the differences in their partition coefficients. Different solvents, or different solvent mixtures, gives different separation. The retardation factor (R), or retention factor, quantifies the results. It is the distance traveled by a given substance divided by the distance traveled by the mobile phase.
In normal-phase TLC, the stationary phase is polar. Silica gel is very common in normal-phase TLC. More polar compounds in a sample mixture interact more strongly with the polar stationary phase. As a result, more-polar compounds move less (resulting in smaller R) while less-polar compounds move higher up the plate (higher R). A more-polar mobile phase also binds more strongly to the plate, competing more with the compound for binding sites; a more-polar mobile phase also dissolves polar compounds more. As such, all compounds on the TLC plate move higher up the plate in polar solvent mixtures. "Strong" solvents move compounds higher up the plate, whereas "weak" solvents move them less.
If the stationary phase is non-polar, like C18-functionalized silica plates, it is called reverse-phase TLC. In this case, non-polar compounds move less and polar compounds move more. The solvent mixture will also be much more polar than in normal-phase TLC.