Apollo and Artemis were two twins born by the king of the gods Zeus and Leto, a daughter of the Titans Coeus and Phoebe.
Leto was a very gracious and loveable deity but was hated by Hera, the wife of Zeus, for having seduced her husband. So when Leto became pregnant and Hera found out, she explicitly forbade any place under the sun to offer shelter to the sinful woman. She even held her daughter Eileithyia, the goddess of childbirth, firmly in her arms to prevent her from supporting Leto on her labor.
Zeus felt sorrow for Leto and transformed her into a quail (ortyx) in order to give birth to their children. However, there seemed to be no place all over Greece willing to offer a shelter to Leto, so she was wandering around desperately and aimlessly...
Finally, Leto discovered a tiny cycladic island close to Mykonos named "Asteria" (or Ortygia, deriving from Leto's transformation into a quail).
This island was beaten by the waves and blown by the wind and didn’t even have a fixed position in the sea, yet it was willing to accept the woman. When Leto settled on the island, the island became firm and its name was changed into "Delos"- "the unconcealed one".
For nine days and nine nights Leto was suffering from strong pains, until on the tenth day, Leto went close to a small lake, leaned against a palm tree, unfastened her belt and gave birth to Artemis, the Greek goddess of the hunt.
Artemis then acted as a midwife to her mother to bring her brother Apollo to the world. For this reason, she was declared as the new goddess of the childbirth, taking the place of Hera’s daughter Eilithyia.