1580s, "serving to portray or symbolize," from French representatif (early 14c.) or directly from Medieval Latin repraesentativus, from stem of Latin repraesentare "show, exhibit, display" (see represent).
Meaning "standing for others, acting as a substitute or agent for another" is from 1620s. Specifically in the political sense of "holding the place of, and acting for, a larger body of people in the government or legislature" it is recorded from 1620s; the meaning "pertaining to or founded on representation of the people, having citizens represented by chosen persons" is from 1640s. Related: Representatively (mid-15c.).
1630s, "member of a legislative body (such as the British House of Commons or the U.S. House of Representatives) who represents a number of others," from representative (adj.). By 1640s in the sense of "example, type, sample, specimen."