The guitarist is a wizard of the fretboard. He can use powerful moves such as power chords (and later on full chords), solos, scales, and can use popular guitar "moves" from throughout rock's history, such as Chuck Berry's duck walk (that Angus Young would later use), Pete Townshend's "Windmill" and Jimi Hendrix's tooth-picking (heh... tooth-picking...).
The bassist is an essential part of any band. Should the guitarist be put out of commission, the bassist can keep things rolling with his rhythmic playing. The bassist can help restore fans (the game's equivalent of HP), and can help bring members back after they've been booed (KO'd).
The drummer is the band's heavy-hitter. The drummer's pounding can steal away more of the rival band's fans, but if a guitarist should focus their attacks on him (or her), he (or she) won't last long.
The singer is the band's most mobile member. Since the singer is least likely to be tangled in cords while moving around stage (the drummer could, but then they wouldn't be doing much drumming), this class can sneak around stage and unplug the other band's amps in a guitar battle, along with taking a beer from an audience member and splashing it on opposing bands (think of the possibilities! I mean, spill liquid all over a guitarist, his input jack and his amp's plug and see what happens).
In case you haven't noticed yet, the classes here correspond to more classical ones. The guitarist is the mage, the bassist is the healer, the drummer is the barbarian, and the singer is the rouge.