Donkey Kong was the product of a Nintendo artist named Shigeru Miyamoto. Miyamoto did the entire game himself (even the music), the only help he got was with the name. He and a manager decided they'd call it "Donkey Kong", Kong in reference to the classic movie King Kong, and "Donkey" was used because their Japanese-to-English dictionary said it meant "stubborn, wily, and goofy.
Another story on how the game's name evolved was that it was supposed to be "Monkey Kong", but due to a barely legible fax transmission, the screenprinters created thousands of pieces of artwork that read "Donkey Kong" instead. Since the manufacturers were in a rush to get the game released, they opted to change the game's title rather than wait for the artwork to be reprinted.
In an arcade market that consisted almost solely of space-based shoot-em-ups, Donkey Kong gets a cold reception from the Nintendo brass. But Shigeru persists on pursuing the project, and since it uses the same hardware as the flaccid selling Radarscope it can be used as a cheap conversion kit for the 20,000 or so units of that game Nintendo has already produced.
Donkey Kong becomes the biggest selling arcade game of 1981.