Enzymes denature at high temperatures because the higher temperature alters the size and shape of the active site so that substrate molecules can no longer fit. The substrate molecules typically fit in like puzzle pieces, but if the shape changes, they can no longer use the enzyme to catalyze the reaction.
Enzymes are catalysts within cells. They are designed to speed up certain reactions by a tremendous amount. There are many different enzymes, each designed to catalyze different reactions. To work, a reactant, also known as a substrate, must bind to the active reaction site of the enzyme. If the target substrate cannot do this, the enzyme is said to be denatured.