"Our Lady of Perpetual Labor" is an orchestral piece from the Season 6 soundtrack.
Claire begins pushing, and Kate remembers the last time she began pushing to deliver Aaron. Confused, Kate continues helping deliver the baby, and continues having flashes of the first birth. Once it's born, Kate hands it to Claire, and both now remember their lives. The two cry together.
Charlie returns with blankets, and Claire now recognizes him. Kate thanks him, though he doesn't understand why. Then Claire takes his hand.
He remembers seeing her the night of the crash. He remembers giving her a jar of imaginary peanut butter. Claire says his name, and he begins crying. He remembers when they first met, Claire cutting his hair and the bjorn he made for Aaron. He remembers their first kiss.
The two kiss. Aaron cries.
Kate asks Desmond what they must do next, and he smiles.
The title alludes to titles for the Virgin Mary within Catholicism, such as "Our Lady of Perpetual Help" and "Our Lady of Perpetual Sacrifice". During the scene, we see Claire go into labor with Aaron - for the fourth time.