Skate punk (also typically referred to as skatecore or skate-thrash) was commonly thought to be an offshoot of hardcore punk music. The reasoning is simple - the music was very popular with skateboarders of the time, and many members of skate punk bands were, themselves, skaters.
There are many different subgenres of punk music, and most of them are derivatives of one form of music or another. For example, skate punk elements can be found in many alternative rock, grunge, and post-hardcore bands.
To identify a song typical of the skate punk style, simply listen! Fast guitars (think Ramones style), 4-note basslines, and surf-music drums are all common elements within the genre. Skate punk songs are upbeat, fast, and desperately try to emulate the feel of skateboarding for the listener.
Because most of the band members and their fans were skaters themselves, the skate punk genre developed its own following much apart from the standard punk scene. You can liken skate punk songs to the aggression found in hardcore punk music, but skate punk deal with very different topics.
The reason skate punk is an offshoot of harcore punk music are because of the bands that made the genre popular throughout the 1980's. Bands like Blag Flag and the Circle Jerks appeared quite popular among skateboarders.
However, the formation of skate punk is usually accredited to bands like JFA and Big Boys, who are thought to be the frontrunners of the skate punk genre as its own viable force within the punk community.
Throughout the 1980's, skate punk continued to grow in popularity, and reached an all time high when the Vans Warped Tour commenced during the 1990's. Eventually, the popularity of skate punk gave rise to the classic grunge sounds of the 90's with bands such as Nirvana being readily accepted.
Because skate punk and grunge music seemed so similar on the surface, many followers of the skate punk genre easily accepted grunge bands as a nice alternative to the music that was already out there.
No matter how you view skate punk as a music form, there's no denying that the culture of the early 1980's and 1990's gave rise to this alternative subgenre of punk music. To this day, elements of skate punk can still be found within the punk scene - all you have to do is listen.