Pet ownership, and cat ownership specifically, has been proven to be beneficial to human health in a variety of ways, including general stress reduction and positive mood alteration in addition to more specific markers of improved health such as lower heart rate and blood pressure. Studies that have covered this topic note that the presence of a companion animal such as a cat has a marked positive impact on human mood. However, getting to the exact root of some of these supposed health benefits isn't easy; it is difficult to determine cause and effect in these situations.
Because some people who are in bad health may not feel able or be willing to take on the responsibility of owning a pet, it could be that some of the studies that indicate a correlation between good health and pet ownership are not actually pointing to causation. That is, it could be that pet owners are a self-selecting healthy bunch to begin with, meaning that studies that seek to find a connection between human health and pet ownership will be successful, but not necessarily because the pet itself is responsible for its owner's good health. Health benefits may be harder to prove in cat owners, who don't tend to exercise with their pets the way dog owners do.