The basic reference here is to the story of Helen of Troy in the Iliad. The story actually begins with Zeus taking the form of a swan and seducing a human woman Leda. Because Zeus was in the form of a swan, Helen, the daughter resulting from the union, turned out to be the most beautiful woman in the world.
A few decades later, Eris, the goddess of strife, was not invited to the wedding of Peleus and Thetis. In anger, she tossed an apple into the festivities labeled "for the most beautiful woman." The goddesses Hera, Athena, and Aphrodite all thought they deserved it. The Trojan man Paris, because he was the most handsome man in the world, was chosen to judge the contest. Hera sought to bribe Paris with power, Athena tried to bribe him with wisdom, and Aphrodite offered him Helen. Paris chose to give the apple to Aphrodite.
Helen at this time was wife of Menelaus, the brother of Agamemnon and king of Sparta. Paris, aided by Aphrodite, abducted Helen, and Menelaus enlisted the rest of the Greeks to sail to Troy (in the thousand ships) to retrieve Helen.
As the story of Helen caused the participants in the Trojan war to be immortalized, Faustus is suggesting that he too will become immortalized if Helen kisses him.