An enzyme is a protein folded into a precise three-dimensional shape. Bonds between the parts of the protein hold it in that shape, and this includes the shape of the active site.
If the temperature gets too high, or the pH becomes too acidic or too alkaline, these bonds break. The enzyme changes shape, and so does its active site. The substrate no longer fits, so the enzyme cannot catalyse the reaction. The enzyme is said to be denatured, and the rate of reaction falls.
Denaturation is usually permanent. Cooling the enzyme down or returning it to its best pH does not bring back the original shape. Enzymes are not alive, so we say they are denatured, not killed.