In Ancient Greece, the God Hermes was a phallic god associated with fertility, luck, roads and borders; he was also known as the messenger of the Gods, and later as the patron of markets and merchants, travellers and athletes. His name is thought to derive from the Greek word herma, a boundary stone or pillar of square rectangular form topped by the head of Hermes, and with ithyphallic male genitals further down on the pillar. These herms were placed at strategic points along roadsides and crossroads, marking boundaries, and also placed outside houses, gymnasia and in markets, in order to ensure the fertility of herds and flocks, and to bring luck.
The example we have here is a copy of a famous sculpture, the Hermes Propylaios (Hermes Before-the-Gates) which stood at the entrance to the Acropolis at Athens. The original, by the renowned Athenian sculptor, Alcamanes, in the second half of the 5th Century B.C., is known to us from literary descriptions, and from later copies. Cf. A. Stewart, Greek Sculpture, Yale, 1990, pp. 267-8, pl. 400, for similar.