Phoebe was a Titan goddess of prophetic radiance, often associated with Selene (goddess of the moon). She, however, had never been referred as the goddess of the moon. The misinterpretation probably comes because her granddaughter Artemis was also called Phoebe, after her, just like her grandson Apollo was called Phoebus. And latin authors were all referring Phoebe as the moon goddess or moon itself, but they clearly had Artemis in mind doing so. That is why the Titaness is often misidentified as the moon goddess. To the Greeks it was pretty simple and obvious that Selene was the correct goddess. Romans on the other hand associated Artemis, Hera and Selene to the moon amongst others, but there was no mentioning of Titaness Phoebe. However, some researchers believe that Artemis (Diana, Phoebe) became known as the goddess of the moon because of her grandmother whom she got the name after. Anyhow, Phoebe was rather associated with being prophetic, like her sister Themis and her mother Gaea. She was also one of the twelve titans who were the descendants of Uranus and Gaea. She was, like all of her sisters, never involved in the war between Titans and Olympian gods, and was spared from being imprisoned in Tartarus. Instead, she took her place at the oracle of Delphi.
Prophet of the Delphic Oracle
She became the third prophet at the Oracle of Delphi, where she was believed to have heard her mother's voices. Her predecessors were Gaea and Themis. Gaea honorably gave away her place to her daughter Themis who then gave it to her sister Phoebe. However, according to Aeschylus's myth, Phoebe had felt like having extreme burden to carry and gave away her place to her grandson Apollo as a present for his birthday, probably to motivate him. Apollo then presided over the prophetic power of light and heavens.
Asteria and Leto
Phoebe consorted with her brother Coeus, with whom she had two daughters. One of the daughters, called Leto, plays an important role in the later ages, in the time of Olympians. In those times, Phoebe had also developed a lust for mortal men, but her affairs never came to any fruition. According to Hyginus, who also mentions Asteria and Leto, she was also the mother of Perses and Pallas by Coeus.
Asteria - Titan goddess of oracles and prophecies. With her cousin Perses, she gave birth to goddess Hecate. She was also very beautiful like her sister and therefore pursued by Zeus. However, in order to escape from his embraces, she transformed herself into an island Asteria, later known as Delos.
Leto - Titan goddess of modesty and motherhood. She had very beautiful eyes, with which she charmed Zeus and he soon got her pregnant. Because of it, she was pursued relentlessly by jealous Zeus's wife Hera who drove her from island to island, preventing her to rest and give birth. In the end Leto was finally provided with refuge by her sister Asteria who welcomed her to literally reside on her.