In psychology cognitive dissonance is describes the tension caused by having two apparently contradictory thought processes simultaneously - wanting to smoke while knowing smoking is bad for you, for example.
The phrase was first introduced by Leon Festinger in his 1956 book When Prophecy Fails. He studied the way believers in UFOs dealt with empirical evidence contradicting their deeply held beliefs. It is also associated with the cognitive development theory developed by Jean Piaget - dealing with cognitive dissonance is a key factor in child development.
In general English the term is often used when describing how politicians deal with 'inconvenient' data - examples can be found on all sides of the political spectrum.