Along with Dike and Themis, wise goddesses of Justice, Nemesis was one of the assistants of Zeus, the king of the Olympian gods who was regarded as the founder of law and order. Her home was at Attic Rhamnus, site of a magnificent sanctuary dedicated to the feared goddess of divine vengeance. Beautiful Nemesis initially was portrayed without wings, but in later descriptions she appeared as a winged goddess. In her left hand she held an apple-branch, rein, lash, sword, or balance. Her symbols and attributes were like those of Tyche (The Goddess of Luck and Fortune): a wheel and a ship's rudder. Her parents were said to be either Nyx (The Goddess of Night) alone without a father, or the Titans Oceanus and Tethys.
Nobody wanted to be hounded by Nemesis, and even to this day her name means:
1.A source of harm or ruin:
"Uncritical trust is my nemesis."
A famous example of the retribution of Nemesis is the story of Narcissus. This man was the beautiful son of the River Cephissus and the nymph Liriope. He was so handsome that all women who beheld him at once fell in love with him. The vain Narcissus, however, only had eyes for himself (you could say he suffered from "I" strain...) and rebuffed all admirers.
One such admirer was the nymph Echo, who saw Narcissus and at once fell in love with him. But the beautiful youth couldn't be bothered with the smitten one, who slowly pined away, leaving just the echo of her voice.
Nemesis saw this and condemned the vain Narcissus to spend the rest of his days admiring his own reflection in the waters of a pool. Eventually Narcissus died and was transformed into the flower that bears his name.
Nemesis is considered by some to be the mother of Helen and the twins called the Dioscuri. It's said that Zeus once fell in love with Nemesis (she had quite a bit of Aphrodite's beauty, and some said she was just as gorgeous) and relentlessly pursued her on land and sea. Leery of his intentions, Nemesis avoided Zeus by constantly changing forms, finally transforming into a goose. Not to be outdone, Zeus in turn took the form of a swan, and from the egg she laid came Helen, the ultimate cause of the famous Trojan War.
Thank you to Myth Man for the lovely description