The habanera is a type of folk music that was popular in Cuba in the mid-1800s. It is quite catchy, and it was imported to Spain in 1875, where it became very popular for a couple of decades. This is where the name habanera actually comes from, danza habanera being Spanish for 'dance of Havana'. (The Cubans had simply considered it a form of contradanza, and had not considered it worthy of separate label).
Of course, most of us don't know this. In most English-speaking counties 'Habanera' refers to the Habanera Aria, AKA L'amour est un oiseau rebelle, from Georges Bizet's 1875 opera Carmen. If you don't recognize the piece (I guarantee that you know it, even if you don't recognize the name), you can hear it here, or if you prefer your classical music a capella and sung by Muppets, here.
Of course, there are other habaneras. The distinguishing feature of habaneras is its short, repeating 2/4 rhythmic figure in the bass line 1. Other habaneras include Sebastian Yradier's La Paloma (here) and Eduardo Sanchez de Fuentes' habanera Tu (here). As these demonstrate, habaneras are usually rather slow, sweet, and not accompanied by French opera.