As I interpret them:
1 - A very unique concept that catches peoples eye. Especially the modular nature of the system is what made it so appealing. Hell, even the neon colours have been so great at give it that uniqueness that definitely helped it get noticed in the mainstream arena.
2 - A brand change. Nintendo put some effort in changing their image by the ways of marketing, house styles, online policies and restructuring. I think that coincided well.
3 - The best launch game ever, which is BotW. Nothing more needs to be said.
4 - A whole year of quality releases almost every month, topped off with an amazing Mario game.
5 - Combining strengths of handheld gaming and home console gaming. Thus having also unified games output.
All these things just gave it a really good boost and momentum has been going since then. Also, the incredible amount of fake hate on the January presentation and attempts to ridicule it just made it all the more popular.
Essay Pro