Since Ériu is represented as goddess of Ireland, she is often interpreted as a modern-day personification of Ireland, although since the name "Ériu" is the older Irish form of the word Ireland, her modern name is often modified to "Éire" or "Erin" to suit a modern form.
With her sisters, Banba and Fódla, she was part of an important triumvirate of goddesses. When the Milesians arrived from Galicia, each of the three sisters asked that their name be given to the country. This was granted to them, although Ériu (Éire) became the chief name in use. (Banba and Fódla are still sometimes used as poetic names for Ireland, much as Albion is used as a poetic name for Great Britain.)
Ériu, Banba and Fódla are interpreted as goddesses of sovereignty.
Different texts have attributed different personal relationships to Ériu. Her husband has been named as Mac Gréine (‘Son of the Sun’). She has also been portrayed as the lover of Elatha, a prince of the Fomorians, with whom she had a son Bres, and as the mistress of the hero Lugh. Both Elatha and Ériu are described in some sources as the children of Delbaeth, indicating they may be half-siblings. Her foster-father in the Rennes Dindsenchas was Codal the Roundbreasted, whose feeding Eriu caused the land in Ireland to heave toward the sky.
The University of Wales' reconstructed Proto-Celtic lexicon gives *Φīwerjon- (nominative singular Φīwerjō) as the Proto-Celtic etymology of this name. This Celtic form implies Proto-Indo-European *piHwerjon-, likely related to the adjectival stem *piHwer- "fat" (cf. Sanskrit pīvan, f. pīvarī and by-form pīvara, "fat, full, abounding") hence meaning "fat land" or "land of abundance", applied at an early date to the island of Ireland. The Proto-Celtic form became *īweriū in Q-Celtic (Proto-Goidelic). From a similar or somewhat later form were also borrowed Greek Ἰέρνη I[w]ernē and Ἰουερνία Iouernia; the latter form was converted into Latin Hibernia.
Boydell, Barra. "The female harp: The Irish harp in 18th- and early–19th-century Romantic nationalism", RIdIM/RCMI newsletter XX/1 (spring 1995), 10–17.