One day when I was young
One day when I was young I watched my father grill burgers. When they were done, he handed me one, telling me it was a Bison burger. He then left.....never came back......I know he may not have been dedicated to his family, but he was dedicated to his jokes.
This is a joke about "dad jokes". Dad jokes are the idea that some jokes are horrible puns, so bad that only a father would tell them to his kids. In American media, the idea that dads tell corny jokes is so prevalent, that metajokes like this one are also popular.
I think that secretly they are excuses to tell corny jokes.
To deconstruct this joke, the thing that the dad said was a pun. An american bison is a buffalo. They are sometimes harvested for meat, and when they are, the meat is pretty lean, and also generally expensive. That being said, a bison burger is something that is within the realm of possibility.
The word bison sounds like "bye son", which is something that you might say to your son before you leave them.
The other part of this joke is black humor - the father left his family for the really lame reason that he was more dedicated to a joke than them. It would be considered absurd if it were not such a sad idea.