Touhou is a danmaku game created by "Team Shanghai Alice", the one person team with it's only member being ZUN. Danmaku means bullet hell in japanese. They are focused on having more bullets than enemies. Touhou is famous for the difficulty of it. There are complex bullet patterns that are sometimes impossible to dodge.
There are also other kinds of games in the touhou project, like Scarlet Weather Rapsody, which is a fighting game. Each of the twenty games has something different about the gameplay. Most games have spell cards, or bombs in them. Bombs are used when you can't escape from the danmaku.