The story of Philomela is given by Ovid in Book VI of Metamorphoses.
The beautiful Philomela is kidnapped, raped, and imprisoned by her sister Procne's husband, King Tereus. To prevent Philomela from revealing what he has done, Tereus then cuts out her tongue. Imprisoned, isolated, and unable to speak, Philomela weaves a tapestry depicting her suffering at Tereus' hands and sends it to Procne. Procne, enraged, frees her sister. The sisters then take their revenge on Tereus, murdering his and Procne's son and feeding the boy's body to the king. When the sisters reveal what they've done, Tereus charges them in fury. Before he can reach them, however, all three are transformed into birds. From the Ted Hughes translation:
Images from this story recur throughout the poem. In his note for line 100, Eliot directs us to an echo of the Philomela story in Part III. The swallow appears again at the end of the poem.