What is a submissive pet?

The person taking on the role as the Pet to the dominate partner is the one answer that comes to mind although a Animal Pet may submissive in character, you don't geerally introduce it as 'My submissive pet'.

YOU! Now lick my furry bunny slippers!

It's not a part black lab dog. She's a bully beast.

A submissive pet is a pack animal that is not the pack leader. Dogs are one of the easiest pets to dominate.
As a general rule, you should always dominate your pet.
In dogs, for example, If you do not dominate your pet, that FORCES them to be the pack leader, whether you know it or not. They will show this in canine mannerisms that you may not even notice. The problem is that they are living in a human world, so they can't lead very well, because they don't understand the human world. Secondly, they can become frustrated when you do not do what they tell you to do. They become a pack leader, in charge of a pack that does not listen to them, and doesn't know how to lead the pack in the world around them.
Dominating your pet, and letting him know who is in charge relieves the pet of the responsibility of having to make decisions for you, that you don't follow anyway. While they may object, at first, to you becoming the pack leader, they will be happier and more relaxed when they don't have the burden.

A turtle.