A travesty is a cheap mockery, usually of something or someone serious, such as a travesty of justice.
A travesty is a silly imitation, like a tall young man dressed up like a little old lady. Travesty and transvestite both come from French travesti meaning "dressed in disguise," so it helps to remember the definition of travesty by thinking of that football player in drag. A travesty can be more than that, though. A travesty of justice, for example, is a court case that makes a mockery of the system, or so you might think if the verdict isn't in your favor. There are lots of examples in literature: the book Don Quixote is a travesty of Medieval Romance.