The complaint is the initial pleading that starts a civil action and states the basis for the court’s jurisdiction, the basis for the plaintiff’s claim, and the demand for relief.

In Plain English:

A complaint is a document that the plaintiff’s attorney writes. It is the first document filed in a lawsuit, and it is the filing of this document that is meant when someone says he will “file a lawsuit.” It includes facts and allegations about what happened, and why the plaintiff is suing the defendant.