A catalyst works by lowering the starting energy that a chemical reaction needs. This starting barrier is known in chemistry as the activation energy of the reaction. Because this barrier is lower, more molecules can react at the same temperature.
The catalyst takes part in the temporary steps of the reaction pathway. It often binds with the starting chemicals to form a short-lived intermediate compound. By the end of the reaction, the catalyst returns to its original form.
Sometimes the catalyst and the reacting chemicals exist in the exact same phase. For example, they might all be liquids dissolved together in one solution. Scientists call this single-phase setup homogeneous catalysis, which is often hard to separate.
Other times, a solid catalyst works with reactants that are gases or liquids. Scientists call this multi-phase setup heterogeneous catalysis, which allows for easy separation. A catalyst only changes how fast the chemical reaction reaches its final balance.
It helps the system reach its chemical equilibrium point much faster than normal. However, it never shifts the actual position of that final balance. It also has no effect on the total energy change of the reaction.
A common student misconception is that catalysts do not participate in reactions. In reality, they actively form and break bonds throughout the chemical process.