A conspiracy theory is basically someone/something trying to cover up what REALLY happened and get people to believe their version of the facts.

For instance:

Some people believe that Lee Harvey Oswald shot JFK. (The official version of the story, fact as we know it)

The conspiracy theory version of that is that LHO was set up, he really wasn't the trigger man who shot JFK, but that the CIA (or the Mafia, or the Irish Mafia) had him assasinated.

The examples are endless, and involve everything from the Masons, the CIA end the Illuminati to mysterious aliens.