Caer Ibormeith was the Celtic goddess of sleep and dreams. In Irish mythology, Caer Ibormeith was a daughter of Prince Ethal Anbuail of Sid Uamuin in Connacht. In Óengus’s dream, which lasted over a year, Caer Ibormeith stood beside his bed though when he reached out for her, she would disappear. Every alternate Samhain she would turn to human form for one celtic day, which begins at sunset, and after that, she would revert back into being a swan, in which form she would remain for a year before becoming human again the following Samhain.
Óengus went in search for this girl in his dreams at the lake of the Dragon's Mouth and found 150 girls chained in pairs, his girl Caer Ibormeith, among them. Óengus was told he could marry Caer if he could identify her in her swan form, he chose correctly and with that Óengus turned himself into a swan and they flew away together, to the Brú na Bóinne/palace on the River Boyne near Slane, which was his long standing place of residence, the pair sung beautiful music as they went, that put all listeners throughout Ireland asleep for three days and nights, Caer would marry with Óengus of the Tuatha de Dannan, and amongst other things, become foster-mother of Diarmuid.
The story of Fionnuala and the other children of Lir shares the motif of transformation into swans, as swans and the associated cranes ("grús") share Irish mythological reverence due to, especially in the latter case, being equally at home in flight, on land, and in water, which made it an especially magical creature able to transistion to otherworlds. Moreover, as the tall Crane stands upright when on land, it was associated with shape-shifting, back into human form.