Castor and Pollux were twin sons born from Zeus and Leda; their sisters were Helen and Clytemnestra. Zeus took the form of a swan in order to seduce the lovely mortal woman Leda, and so the children emerged from eggs. Leda also slept with her husband Tyndareus on the same night, so she had a mix of human and mortal children from both of her consorts. Castor is usually regarded as the mortal child of Tyndareus, while Pollux is the immortal child of Zeus. When Castor was killed, Pollux chose to share his immortality so that they could stay together, so Zeus made them into the constellation Gemini, "The Twins."
You can also find more myths and legends for the week of June 17-23 here. For more information and links to the actual javascript code, see the Myths & Legends Widget Reference Page.