Kitten play is a sub category of pet play - which is a BDSM practice. There is a lot that goes into it, but
generally speaking, Kitten Play is a practice which involves a dom & sub (dominant and
submissive). The pet, or in this case kitten, is the submissive, while their master, owner, or guardian is the dominant. A large part of kitten play, and pet play, is feeling like you have someone to
take care of you - to rely on. When acting in kitten play, the submissive will meow, bite, scratch, or an other cat like behavior towards the dominant. The dominant will play with their kitten, and reward them for being good. Although, the full system of punishment & reward is a part of this practice.