Keeping a close eye on what goes into and out of your cat's body can be a good indicator of its health. You may notice that your cat isn't eating as much as before, but you also need to know the context. For example, does he just seem uninterested in food entirely? Or does he come running as usual for his food but then eats little (if any) of it? In the first case, it would be completely correct to say your cat has no appetite. In the second, he has an appetite but something is making him feel like he can't eat very much.
A cat who hasn't been eating well may also not be drinking enough and could become dehydrated. To check whether your cat is getting enough to drink, gently grasp the skin between his shoulder blades, pull up slightly, and open your fingers to let go. If the skin snaps back into place immediately, your cat is well hydrated. If not, your cat could be dehydrated and may need to get fluids at your veterinarian's office to prevent serious harm. On the other hand, if your cat is suddenly drinking more water than usual, that could also be a sign of a problem.
It's usually not polite to talk about elimination, but it's important in understanding the health of your cat. Are his stools well formed, soft or loose? Is there any trace of blood in his urine or feces? Is there mucus in the stool? Even things like a change in color or odor can be important.
Of course, eating and elimination are two sides of the same coin (or two ends of the same digestive system, to be more accurate), so pay attention to how they go together. For example, if your cat has a ravenous appetite but doesn't seem to put on any weight (or actually seems thinner), that should alert you to a possible problem. If you've noticed big changes in your cat's appetite or elimination habits, take him to the vet to determine the cause of the problem.
Now that we've gotten past the messy part, read on to find out why simply petting your cat can reveal how he's feeling.