Habanera is the name often given to the Cuban genre contradanza. This was itself adapted from an earlier French form called contredanse. This was a type of partnered folk dance and there were variations of it in several countries, but it was brought to Cuba in the late 18th century by French settlers. A new, Latin American form developed in Cuba in the early 19th century, in fact the earliest known example was written in 1803.

In Cuba itself the name Habanera is never used for the contradanza genre. Habanera actually refers to the characteristic rhythm of the genre, which is based on two beats and is also known as the congo, tango or tango-congo. It's the basis of a lot of Latin music. A famous example is the Habanera from Bizet's Carmen ('L'amour et un oiseau rebelle'), so called because it is composed in the Habanera rhythm. you can listen to it here.