Cats play fight when living in groups and sometimes even play fight their owners. Play fights are a natural, healthy behavior in most cats and owners should let their cats fight, so long as it doesn't turn aggressive.
Instinctual Need
Many cats play fight due to an instinctual need. Cats are naturally hunters in the wild and must train and hone their ability to defend their territory and take down prey in order to survive. The house cat still experiences these natural urges, and may feel the need to develop these skills with another cat (or even a human). The other cat will understand what's going on and will willingly participate in order to hone her own skills as well.
Territory Defense
Some of the instances of cats play fighting are more than just honing skill - they really are examples of the cats defending their "territory," even inside a house. A cat could defend what it views to be its space in the house or its toy or food. When engaging the other cat in a fight, the intent is not to harm the other cat (so long as the cats usually get along), but to put her in "her place" and warn her to stay away from that thing. If the other cat actually wins the play fight, the other cat may "win" the right to share or take over that item or place.
Burning off Energy
House cats have excess energy that wild cats burn off naturally in the course of hunting for food and defending territory. The house cats need to burn off this energy, and play fighting is one way in which the cats can do so. If a cat feels the sudden urge to burn some energy, she may do many physically demanding behaviors, such as running around the home, playing with toys or engaging other cats in activity by play fighting.
Fighting Boredom
Cats play fight when bored as well. If their attention is not otherwise occupied, they could start a play fight simply to engage another cat and have something to do. Kittens especially have excess energy and a more piqued desire to stay active. They like to pick play fights with older cats, although some older cats may tire of this behavior and scare the kittens away.
When to Step In
Owners can usually tell the difference between a real fight and a play fight if they watch carefully. Aggression between two cats typically involves arching of the backs, growling and hissing. Cats that are truly fighting will pull out their claws, which usually is not the case in a play fight, and screech at one another. Sometimes cats that are just being introduced to another must get over their aggression naturally, but if the fights are consistent or especially dangerous, the owner should separate the animals.
Sometimes the call to step in is more subtle than what one encounters during a display of aggression. If one cat gets injured or one becomes sexually aggressive, the owner should break up the encounter, even if originally it seemed as if the cats were play fighting.