Simplified, this is the notion that words themselves can perform actions--"I now pronounce you man and wife" does not simply state to the congregation that the couple is married, it is the actual act by which the two are legally conjoined. Similarly, "I christen this ship the E2," "I bet you five dollars," etc. This idea was originally developed by a language philosopher named J. L. Austin (you should read his How to Do Things with Words). Originally, he drew a divider between performatives and constantives--those things which only convey information.
He soon threw out this distinction in favor of a better one. After all, he argued, even something like "My plane arrives at 8:00" has performative levels to it--by stating that, you are attempting the action of trying to get the listener to come pick you up, or something. In this new distinction, utterances have three levels: locutionary, illocutionary, and perlocutionary. The locutionary level is that used by traditional linguistics and simply conveys information. The illocutionary level is the subtext: in this example, "Come pick me up." And the perlocutionary is what the speaker is trying to accomplish by his words--for the listener to arrange his schedule around picking him up and then actually doing so.