Reggaeton is a a type of Latin American dance music (not dance music in that it is electronica, but I would consider it more closely related to techno than rap). It has a very strong backbeat, is rather repetitive, and the singers tend towards high energy rather than technical skill. Most of it is sung in Spanish, although you find English and English/Spanish mixes.
Reggaeton (AKA Reggaetón or Reguetón) first appeared in the late 1990s. It was a mix of bomba and plena, hip hop and rap, and some reggae. (The reggae influence doesn't make much of a mark on the music, but the basic beat is said to have originated in the Shabba Ranks reggae song Dem Bow). Reggaeton lives primarily in Puerto Rico and the Dominican Republic, but has been spreading outwards since it's inception. I first heard it in Cape Verde (where I was told it was Batida music from Angola), and it's well known in America's Latino populations.
Reggaeton's 'official' dance is perreo, a grinding dance with the girl in front with her back to the boy. "Perreo" refers to doggy style, and the dance can be rather explict.
If you are interested in hearing some, the most popular song as of this noding is probably Gasolina by Daddy Yankee. It's easy to find on-line (that is to say, download illegally), and sounds exactly the same as all the other regaeton, except better. My personal favorite band is La Factoria, a group from Panama that has had a couple big hits, most notably Perdóname and the ever-popular Papi Chulo.
Ichiro2k3 says re Reggaeton: if you want to hear the reggae influence you'd probably be better served listening to older reggaeton but if you want newer stuff there is a lot of reggae influence in DJ Flex's first album, for example (e.g. "sin tu amor")