Every type of chromatography has two parts. The stationary phase stays still. The mobile phase moves through or over the stationary phase and carries the mixture with it. In paper chromatography the paper is the stationary phase and the solvent is the mobile phase. In thin layer chromatography the stationary phase is a thin layer of silica on a plate and the mobile phase is the solvent. In gas chromatography the mobile phase is a gas and the stationary phase is a liquid or solid inside a long column.
The substances separate because each one is distributed differently between the two phases. A substance that is more soluble in the mobile phase spends more time in it, so it travels further. A substance that is held strongly by the stationary phase spends more time stuck to it, so it moves only a short distance. Because every substance has its own distribution between the phases, they end up at different places.