From the article that kat linked to above:

"Cancer cells emit different metabolic waste products than normal cells," Broffman said. "The differences between these metabolic products are so great that they can be detected by a dog's keen sense of smell, even in the early stages of disease."

If dogs can smell it, maybe cats can, too.

And if cancer emits special chemicals, the failure of various organs probably does, too.

My vet taught me that when an animal is experiencing kidney failure, its breath smells like urine.

There's no need to assume the cat in question has any psychic ability. Probably just a good sense of smell.