Touhou is a bullet-curtain shooting game. Basically, enemies shoot bullets, you dodge the bullets, then destroy the enemy. It is a doujinshi* game created by Team Shanghai Alice, which consists of a single person: ZUN. He did the artwork, story, music, and programming for all of it, except for two fighting games which he partnered with another group. Usually the Touhou games are extremely challenging, the normal mode being more difficult than a standard game's "Difficult" mode. So far there are 12.3 (lol) Touhou games.
*Doujinshi basically means a random person made it, rather than a well known company.
Just search it up on google. You'll find it in a split second. Wiki has a ton of info about it too.
Here are some topics that were already created that are about Touhou:
Touhou - Prepare for Bullet Hell!
Cirno Day