The Judgement of Paris is a story from Greek/Roman mythology, in which the legendary roots of the Trojan War can be found. As with many mythological tales, details vary depending on the source, but one compendium of details is:
Zeus (Jupiter) held a banquet in celebration of the marriage of Peleus and Thetis. Left off the guest list was Eris (goddess of strife), and upon turning up uninvited she threw an apple on to the table and invited the most beautiful to pick it up. Hera (Juno), Athena (Minerva) and Aphrodite (Venus) contended for the apple, and eventually Zeus declared that Paris, a Phrygian mortal, would judge their cases.
All three of the candidates attempted to bribe Paris; Hera offered to make him a king, Athena offered great knowledge, and Aphrodite offered the love of the world's most beautiful woman. This was Helen of Troy, wife of the Greek king Menelaus. Paris accepted Aphrodite's gift, receiving Helen and the enmity of the Greeks. The Greek King Agamemnon's expedition to rescue his vassal's wife is the borderline mythological basis of the war with Troy
The Judgement of Paris and its fallout figures in any number of artistic endeavors, including the Portland Vase, the Pyxis Pot, Lucian's "The Judgement of the Goddesses", and Peter Paul Rubens' "The Judgement of Paris". Interestingly, the most important artistic work on the Trojan War, Homer's Iliad references Paris' stealing of Helen in a rather oblique way involving only Aphrodite; some commentators have suggested that it is playing off a different legend of Paris, now lost.