c.1600, "group of students," from French classe (14c.), from Latin classis "class, division, army, fleet," especially any one of the six orders into which Servius Tullius divided the Roman people for the purpose of taxation; traditionally originally "the people of Rome under arms," and thus akin to calare "to call (to arms)," from PIE root *kele- (2) "to shout" (see claim (v.)).
School and university sense of "course, lecture" (1650s) is from the notion of a form or lecture reserved to scholars who had attained a certain level. Natural history sense is from 1753. Meaning "a division of society according to status" (upper, lower, etc.) is from 1772. Class-consciousness (1903) is from German klassenbewusst.