Well I took it further from the prompt for laughs and giggles, a pet with superpowers. Oh man, my pet would cause so much harm. I think of movies like Honey I Blew The Kids, and animation like Super Pets and The Minions. If my pet was to understand one thing, of course it would be I love you and I am your master and to under every command I say translate to an action to do.
It’s such a weird question, of course you want you pet to understand language and emotions. But surely, it’s a pet, it doesn’t have school and trainings and control of life like humans, but hey common communication, understanding and feelings would be interesting. Lastly, they need to know baths are not bad, they should want to do so, and help me make the best pet youtube channel in the world. :) ha ha