Explain, in general, how a catalyst works

A catalyst is a material that can speed up a reaction, but reamins chemically unchanged at the end of the reaction. A catalyst works by providing the reactants an alternative route of reaction with a lowered activation energy barrier.  The total activation energy barrier is "divided" across several cascading reactions, hence reducing the activation energy barrier of the rate-limiting step - this increases the overall rate for the whole reaction. 

A way to think how a catalyst works is by imagining climbing from the ground floor to the top floor via two possible routes; by jumping or stairs. The height difference can be thought of as the activation energy barrier. Jumping vertically might be possible, but would take a lot of energy with few successes. On the other hand, taking the steps requires less energy and makes the process faster - stairs are therefore catalysts for elevating you to new heights!