A catalyst is a chemical substance which can speed up the rate of a chemical reaction without being consumed itself. This happens due to the activation energy required for the reaction to take place getting reduced.
Catalysts can be substances which are in the same state as that of the reacts or they can have a different state. State here is used with reference to solid, liquid or gas. An example of catalysts which have the same state are enzymes, which speed up, and in many cases allow, reactions within our body to occur. Both the reactants as well the catalysts are in the liquid state. An example of a catalyst in a different state as the reactants would be the platinum-rhodium catalyst used in catalytic converters of cars to break down nitrogen oxides into nitrogen and oxygen. The catalyst here is solid and the reactants are gases
The working of catalysts usually follows this path:
Two substances X and Y have to react to yield Z. The direct reaction of X and Y requires a lot of activation energy. The catalyst works by forming an intermediary with X or CX; Y reacts with CX forming CXY; this is converted to CZ and finally Z is liberated freeing the catalyst C.
The catalyst is able to facilitate the reaction of X and Y as it requires lesser energy to form CX and for Y to react with CX to finally result in Z than the direct reaction.