You wouldn't guess it by listening to today's Ska music, known as Third-Wave Ska, but traditional Ska music was actually a precursor for Reggae. Born in Jamaica in the 50's from Mento, Calypso, American Jazz, and R&B (worldmusic.com), Ska is so-named because of the "ska, ska, ska" guitar sound which carried into Reggae.
Traditional Ska music is dancing music. It's upbeat, fast paced, and generally fun. That "ska" sound holds the off-beat, while horn and saxophone parts carry the melody. Its simply fun to listen to. The beat begs to be picked up and danced with.
Two-tone succedded Traditional Ska, implementing punk sound and energy while still honoring the "ska" beat and horn parts. Headed by the The Specials and Jerry Dammers, it was a 1970's revival, adding new vitality to the genre. It is a natural transition to Third-wave ska, which is also known as Punk Ska.
Third-wave ska marked the growth in horn sections. In many ways, it was a return to the more traditional stylizations of Ska music, but had its own contemporary influences. Starting in the 80's and building in the 90's it eventually evolves into modern ska as we see it today.
The most modern interation of Ska is Ska Punk, or Post-Third-wave Ska. It more fully realizes the potential behind combining punk influences and the horn sections of ska. It has, in many cases, abandonded the orignal "ska" sound and jamaican vocal style, essentially making it punk with a horn section. Despite this deviation from the original sounds of Ska, it certainly holds its own amongst the genres.