1580s, "to investigate, examine," a back-formation from exploration, or else from Middle French explorer (16c.), from Latin explorare "investigate, search out, examine, explore," said to be originally a hunters' term meaning "set up a loud cry," from ex- "out" (see ex-) + plorare "to cry."
But second element also explained as "to make to flow," from pluere "to flow." Meaning "to go to a country or place in quest of discoveries" is first attested 1610s. Related: Explored; exploring.