Progressive music is the natural, evolutionary progression a genre.
Originally coined for progressive metal (aka prog metal), it is now used for almost every major genre. (On a side note listening to progressive music is like watching a good movie).
Progressive metal is defined by much lengthier songs, averaging 8-10 minutes each (with instances of 20, 40, and 60 minute songs that are also played live) with heavy emphasis placed on the technical aspects of playing instruments, a continuance of the progression from classical music that it's parent genres, thrash/speed, and heavy metal introduced. The lyrics are an advancement of the poetic harmony introduced in the lyrics of the speed/thrash metal bands Megadeth, Metallica, Slayer, Anthrax, and Exodus. Also...progressive music tends to well up emotional responses very well, especially live.
The progressive metal movement was started by Fates Warning as they began to move from the Iron Maiden like sound of their first two albums. The term however was coined to describe Dream Theater, who is considered by most to be the band that defined the genre.
To name a few (alpha order so as to offend nobody 8o)...Angra, Dream Theater, Enchant, Evergrey, Fates Warning, Labyrinth, Opeth, Savatage, Shadow Gallery, Spiral Architect, Sun Cage, Symphony X, Threshold, Vanden Plas