Enzymes perform more than one function: some are involved in digestion, others in storing or utilizing energy, and some in maintaining a suitable internal environment, or homeostasis. It is the last group which I will discuss. These enzymes can attack substances, foreign or otherwise, and render them harmless. This can help keep a cell from being broken apart by some chemicals.
On the other hand, homeostasis affects the way enzymes function. For example, if the pH swings out of the normal range for a cell, the acids or bases might denature the enzymes, changing their shape or breaking them down. A change in temperature can have a similar effect on the enzymes.
In living things, buffers can help maintain a constant, suitable pH. Enzymes can eliminate foreign substances (like H2O2). And different organisms control temperature in different ways (some rely on outside conditions to change internal temperatures, like a pig rolling in mud to cool off. Humans have sweat glands which use evaporation to cool them).
In conclusion, you can now see why homeostasis and the function of enzymes are closely related. Enzymes help maintain homeostasis. And homeostasis keeps enzymes functioning. In these ways the two share a close relationship.