Nintendo had released their first home video game console, the Famicom, in 1983 in Japan. It launched with home versions of Donkey Kong, Donkey Kong Jr. and Popeye (which Nintendo eventually got the license for). Shortly after this it got a home version of Mario Bros. as well. But it lacked a killer title, something totally new.
Miyamoto was assigned to come up with another game, one even more innovative than Donkey Kong, in time for the launch of the Famicom (redesigned and renamed the NES) in America, where a huge video game crash had just taken place due to the deluge of terrible Atari games putting customers right off gaming.