Old English team "descendant, family, race, line; child-bearing, brood; company, band; set of draft animals yoked together," from Proto-Germanic *tau(h)maz (source also of Old Norse taumr, Old Frisian tam "bridle; progeny, line of descent," Dutch toom, Old High German zoum, German Zaum "bridle"), probably literally "that which draws," from PIE *douk-mo-, from root *deuk- "to lead."
Applied in Old English to groups of persons working together for some purpose, especially "group of people acting together to bring suit;" modern sense of "persons associated in some joint action" is from 1520s. Team spirit is recorded from 1928. Team player attested from 1886, originally in baseball.