Donkey Kong is the titular antagonist of the arcade game. He kidnaps Pauline (Mario's love interest) and climbs to the top of a building made up of ladders and glider. The player (Mario) had to climb the ladders and get to the top, avoiding barrels, fireballs, and spring-like objects.
The original Donkey Kong that appears in the Mario arcade games isn't the same as the one who appears in the Donkey Kong franchise, and Mario spin-off games. After he grew older, his name was replaced by Cranky Kong, while the new takes on the "Donkey Kong" role. Unlike Cranky, the new Donkey Kong appears to be on good terms with Mario.