A series of danmaku shooting games made by one guy under the name ZUN. He is worshiped as a God on many image boards who view his work as some of the best shit ever.
Basically the game involves you flying around as a loli dodging bullets of many a color (blood red, royal blue, cum bubble white, etc.) while laying the beat down on other lolis who want to destroy you for their own personal gain. Usually.
Touhou is popular mainly because of the HUGE amount of fan works and shit other people put out for it, doujins, fan games, and even a trading card game. Tons of inside jokes revolve around the series and charicters and a lot of it is frowned upon outside the small circle of fans by people calling players and fans of the game "pedophiles" and "touhoutards" /a/ and /v/ boards on 4chan say they hate it but only because the majority of them suck nuts at it.
There is a Touhou Wiki and a deticated Touhou image board on Wakachan.
"I can't get past Touhou 8: Imperishable night stage 4 on easy guys." -typical /a/ poster.
"lulz, go back to tetris." -Typical /a/ troll. (Usually sucks at Touhou as well.)