Many different species yawn: humans, cats, dogs, rabbits—even birds, snakes, and fish.
Cats' yawns are more dramatic than human yawns because they can open their mouths wider (and show off those impressive fangs). Are they getting more out of their yawns? We can only guess.
Like humans, cats yawn when transitioning between sleep and alert states; indeed, yawning is a distinctive part of a cat's wake-up routine. Cats and humans may also be prone to yawning when cooling down after energetic activity.
Cats sometimes yawn as a way to peacefully end a standoff with another cat or other animal, as if to say "whatever." This may also be a subtle show of dominance.
Cats don't yawn out of boredom, so don't take it personally if a cat yawns while in your company.
Why exactly do we—cats, humans, and other species—yawn in the way we do? Why, without thinking about it, do we fully open our mouths, partly close our eyes, take a big breath and then exhale? Scientists aren't sure. One school of thought was that yawning gives us a quick oxygen boost when our body needs it, but due to a lack of evidence that theory has fallen from favor.
One benefit of yawning, though probably not its primary purpose, is that it provides a gentle, relaxing stretch of the jaw muscles.
When one human yawns, that often triggers others in the room to yawn. Some people have reported that when they yawn, their feline companions occasionally yawn as well, in copycat fashion. Interspecies sympathetic yawning may indicate a close connection between fellow yawners.
Among humans, simply talking about yawning can produce yawns. Come to think of it, perhaps there's a kitty around who feels like cuddling and joining you for a catnap.