Poseidon is the god of the sea, horses, and earthquakes. He generally appears as a strong old man (but not as strong as Zeus). He has a rather full beard and a stern expression on his face. He is usually depicted throwing a trident to spear some fish.
Poseidon was just as promiscuous as his younger brother Zeus. Despite these dozens of relationships, he fathered Triton (his trumpeter) with his Nereid wife Amphitrite. He also raped Demeter, who bore Persephone (goddess of flowers and wife of Hades). His human lover Libye (yes, the namesake of Libya) gave birth to Agenor (father of Cadmus and Europa) and Belus (father of Danaeus and Aegyptus); these two men were the mythical progenitors of many Mediterranean races.
Poseidon has one noteworthy tale to tell, that of the naming of Athens. He and Athena vied over the name of King Cecrops's new city. Poseidon offered to give the people horses (his new creation) and a saltwater spring. Athena offered a grove of olive trees. Horses wouldn't do well in that hilly country, and salt water isn't fresh, so the people named their town Athens, after Athena, and received their well-known symbol in return.