http://touhou.wikia.com/wiki/Touhou_Wiki
Touhou. A Japanese danmaku vertical side-scrolling shmup. Or, for ease of reference, an STG or Bullet-Hell.
The series is known for its beautiful music, and the fact that every game is created by -one- person, ZUN.
The story line is....erratic at best. But in a game like this, story isn't really that important, now is it?
But...let the games and music speak for themselves. The link at the beginning of this post is the offical Touhou wiki, and any questions you may have should be answered there.
I myself am a -huge- touhou fan, and have beaten most of the games, a few on the hardest difficulty level, which if you search for videos on youtube, you will realize how difficult that can be.