His bass playing was very original and influential, at least in Progressive Rock. Most rock bassists both then (the 1960s-70s) and now use the bass as a rhythm instrument. Squire instead used his bass as melodic instrument, something previously unheard of in rock music. In many ways, his virtuosic playing, with it's distinctive bright and cutting tone, made the bass a lead instrument, fully the equal of the electric guitar.
He was also a talented songwriter, contributing much to the group's now classic albums and was up until now the only constant in the infamously ever-changing line-up of Yes. Here's Long Distance runaround from the album Fragile. This segues into the track The Fish (Squire's nickname, due to his long baths), where as the liner notes say "each riff, rhythm, and melody is produced by using the different sounds of the bass guitar".