Latin was a style of Earth music that originated from the Latin culture.
Mariachi was a type of music with an uptempo Latin beat; whereas the Spanish guitar was more of a gentle Latin beat. In order to pass the time while en route to Risa in the Type 15 shuttlepod Onizuka, Geordi La Forge requested to listen to some Latin music. (TNG: "Deja Q", "The Mind's Eye")
The mambo was also a type of Latin dance music. Jean-Luc Picard requested such music while the USS Enterprise-E visited the Ba'ku planet in 2375. (Star Trek: Insurrection)