In contemporary usage, burlesque is a playfully nostalgic form of striptease — think fans and feather boas rather than explicit nudity — but this is just the latest form of an ironic style of entertainment dating back to medieval times.
Burlesque comes from burla, Spanish for "joke." Comedy has always been an essential part of burlesque art, but it's comedy of a particular kind. Burlesque is satirical, and it uses exaggeration that can be extreme. Early examples of burlesque in English literature can be found in the Canterbury Tales. By the eighteenth century, the word was used to describe often risqué parodies of serious operas or plays. Burlesque became associated with striptease in the music halls and vaudeville theaters of nineteenth-century America.