2 types of games can be classified as a "clciky game", at least for me.
1) the type Ilirion linked to. The over all objective of the game is to get other people to click your stuff. Every time someon else clicks your stuff, you get rewarded. More clicks, more stuff, etc.
2) other type of clicky game is games like Diablo, in which, you have to spam the mouse button to do stuff as stuff only fire off every time you click.