What genre
Prog is it's own style because he has influences coming from literally anywhere. From blues to jazz, clasical to orchastral(?) anything can influence prog. Prog is an extremely diverse style, it is all about pushing boundaries of creativity while taking time to construct difficult chord structures. Progressive is what it says it is; Progressive. Throughout a prog song the sounds can vary and build which often accounts for the length of prog songs. Prog is well know for it's long songs, many heading well over 6 minutes in length.
Good bands to check out:
King Crimson
Yes
Jethro Tull
Radiohead
Pink Floyd
Tool
Rush
Genisis