Priapos is the ithyphallic god of animalic and vegetabilic fertility and generally a bringer of mercy and protector against evil, originated at the coast othe Helespont, especially in Lampsakos. The city of Priapos is named after him. His name is related to Priene, Priamos and the name of the Bithynean war god Prietos. Probably together with Alexander's Crusade his cult spread in the Greek world and absorbed various local deities like Phallos in Attica or Mutunus in Rome, which he replaced. Primarly coarse formed, red coloured wooden statues were sacrified to him, so-called Hermes columns (a bust on a column). Typically was his position in Lordosis (leaning back) with erected phallos.
In his function as fertlitity god he acted positively aiding as well as saving against harm. In Roman times his role was limited as garden god. But he was the protector of wanderers and in Greece patron of sailors and fishermen too. His sanctuaries were artless and imbedded in the landscape. As heir of the sepulcric Phalloi he was grave guardian too. This directs to a deeper meaning. Occasionally he became even an All God. In Lampsakos donkeys are sacrified to him which leads to mythological explanations, f.e. the proverbial horniness of donkeys. From the graffiti on the walls of his sanctuaries a separate poetic genre developed, the Priapea and the Priapean measure.
Priapos was the son of Aphrodite and Dionysos born in Lampsakos in Mysia, referring to other sources of Adonis or even of Zeus himself. When Aphrodite saw how ugly her child was looking, with big tongue, thick belly and exorbitant member, she threw it away and denied it. It is said that the reason for his deformity was the envy or jealousy of Hera. She should have touched the pregnant belly of Aphrodite with evil magic hand. A herdsman should have found the child and brought it up because immediatly he has assumed that this being could be important for the fertility of plants and animals. Not until Roman times he changed into a bizarre garden god and a kind of scarecrow. So it was assigned to him that he tried to rape the sleeping Hesta but was betrayed by the cry of an ass. In Bithynia it is said that he has educated the young War God Ares whom he first has teached dancing and thereafter the war handcraft. So he rather was a warlike god, and one of the Titanes. For this reason he belongs probably to the series of pre-hellenic, semi-animal teachers of gods, like Kedalion, Chiron, Silen or Pallas.
Naturally the depiction of Priapos generates amusement but even in Christian times there were Priests, Priestresses and whole societies dedicated to Priapos. Priapos had mysteries and his worship was related to and influenced by Dionysos. Lampsakos was the most important city of the Priapos cult, because he was reputedly born there. On a coin of Lampsakos Priapos is not depicted as a dumb and horny garden dwarf as usually but with Thyrsos and Kantharos, the attributes of Dionysos!
Sources:
Karl Kerenyi, Die Mythologie der Griechen
Der kleine Pauly