Green River had little impact outside Seattle, but the impact they had on the music made in Seattle would eventually be felt around the world, through their influence on both their contemporaries (Soundgarden, The Melvins) and later Seattle bands (Nirvana, Alice in Chains), on their labelmates at Sub Pop, and through the bands who would form when the band split up (Mother Love Bone, Pearl Jam, Mudhoney).
They were possibly the first band in Seattle to mix metal and punk (as well as glam rock), leading to the sound known later as "grunge"--and Mark Arm, the group's singer, is widely credited as being the first person to use the term, though not in relation to the sound it has come to signify.
The members were Mark Arm (vocals) and occasional guitarist Steve Turner, who went on to Mudhoney; Jeff Ament (bass) and Stone Gossard (guitar), who went on to Mother Love Bone and Pearl Jam, Bruce Fairweather (guitar), who also went on to Mother Love Bone, and Alex Vincent (drums).
Steve Turner was the first member of the band to leave, citing his dislike of the metal leanings of the rest of the band. Later, Mark Arm was to cite these same reasons as part of the reason why the band split. His main gripe, however, was what he saw as being the careerist attitude of bassist Jeff Ament in particular. While the rest of the band seemed to mostly share the wish to sign to a major record label, Ament attracted Arm's ire at one of the bands final shows by sending out all the backstage passes to A&R people - Arm wanted to give some to his friends. That none of the A&R people who received invitations turned up can't have helped matters much.
This argument would later lead to the antagonism between Kurt Cobain, a friend of Mark Arm, and Pearl Jam; though Kurt later befriended Eddie Vedder, he still held Jeff Ament and Stone Gossard in low regard.