Kitten play is similar to PonyPlay or Puppy play, it's a sub strand of the BDSM community in which the participents enjoy dressing as an animal and being treated as such in various humiliating activites which can include:
Drinking and eating from a pet bowl
Crawling on all fours, often required to be naked
Wearing a collar, often with spikes or bells
Taking commands from your Master/Owner/Trainer
Sleeping in a doggie/pet bed or on the floor
Going for walks on leash
Being required to use a litterbox
Being punished for not following commands
Can be taken to other animal play events and participate for prizes (See links for some of the events)
Dressing as the animal in ears and tail, often a buttplug is used for the tail