Phoebe is a Titan goddess of intellect and prophecy because she controls the Oracle at Delphi.
Phoebe was a daughter of Uranus and Gaea, but not directly involved in the overthrow of Uranus by her brother Cronos. She was not very active in mythology, but her lineage is the most interesting part of her story. She married Coeus, the god of the celestial axis. With him, they had Asteria and Leto. Asteria was the mother of Hecate; Leto was the mother of Apollo and Artemis, making Phoebe their grandmother.
She was considered to be the goddess of intellect and prophecy because she received control of the Oracle at Delphi from Themis and became the third prophet. She eventually gifted this to her grandson Apollo. She is often depicted with the moon as her symbol.
Uranus and Gaea
Goddess of Intellect and Prophecy