A courante (Italian: corrente) is a dance that was popular in Baroque music in the 17th and early 18th centuries. The word comes from the French word for to "run".
The courante was a fast, running dance with 3 beats in a bar (the time signature was often 3/2, although sometimes it was 3/4). During the 17th century the French courante started to become slower than the Italian corrente, and it often had more counterpoint (imitating parts). However, this was not a strict rule, and the courantes that Bach wrote were both Italian and French in style, and sometimes he called them "courante" and sometimes "corrente".
Composers of the Baroque period often composed a group of several dances. This was called a suite. There was usually an allemande, then the courante was the second dance, followed by a sarabande and a gigue and sometimes one or two other dances or as well.