I've read about it a little and heard about being a pet. I'm submissive. What is a pet?
The term "pet" can apply to variety of things, in it's most basic form simply as a term of ownership of a sub as in "you've done well my pet".
It could also apply to some people who adopt a pet persona such as a cat, dog or fox for instance. This can involve "pet play", being walked on a lead, eating from a pet bowl and even wearing a tail often attached to butt plug.
As with most kinks there aren't any really hard and fast rules here but in general it's going to involve some pet like behaviors.
