OP, look into how chromatography works. It's interesting and informative as well as helpful if you're struggling with this concept. With chromatography, it's all about affinity. The solute will have some affinity for the silica gel that's inside the TLC paper. So it will bind to that silica. When you run a solvent up the TLC plate, it will compete with the silica gel for binding to the solute. If a component of your solute "likes" the solvent better, it'll move up the plate with the solvent. If it doesn't like the solvent, it'll stick to the silica and appear to move less.
In chemistry, we use TLC plates to determine what solvent gradient to use when we're running a column separation. So say you have components A, B, and C in your solute. You do a TLC and use a 15% EtOAc/85% hexanes solvent. The spot on the TLC plate separates into three spots when you run the plate. The EtOAc is there to introduce polarity into your solvent so that the solute, which is stuck on the silica, will be washed off by the solvent. If the solvent is polar enough, it will outcompete the silica for binding. If you get a good separation, then that means that the 15% EtOAc composition is good enough for your separation and you can put your compound through the column. If not, then you fiddle with the composition - maybe 25% EtOAc - and try it again until you find ideal separation.
If, on the other hand, the spot is moving right along with the solvent front in all of those trials and you try 100% hexanes and it still runs with the solvent front, then all of your components are pretty nonpolar and you should probably try using a reverse-phase column. In those columns, instead of packing with silica, you pack with a nonpolar material and you run a polar solvent through it. A common solvent combination is H20 and acetonitrile. You start with 100% H20 and run a gradient. This is how an HPLC usually works.