A donkey is just one of the many negative slang terms people use to describe poor players. Other names include, fish, donk, idiot, sucker, etc.
I like this definition.
A poker donkey is a bad player, or is he? A poker donkey is a gambler. Not just any old gambler though. The poker donkey will hit their gut shot straight, seven high flush, and miracle full-house after a fourth street flush. The poker donkey is a terrible gambler. The poker donkey will gamble with incorrect odds
and hit their miracle card.
A poker donkey does not know any better. Donkeys like to play and they will get paid at your expense. You can expect to find a poker donkey at the lower limits of poker. Usually they will go on good runs of cards. The donkey will run so good that they will be mistaken that they are actually good at poker and berate other players to their fine playing skills.
But, like all donkeys they finally end up on the rail watching other donkeys play. The poker donkey will often be mad and sulk and blame the cards for the absolute terrible run of bad fortune. It is only then that the poker donkey will dig deep to gain knowledge of the game.