Ériu

The personification of Ireland and goddess of sovereignty. She is presumably also known as Flaith Érenn, the woman of the cup in the story Baile in Scáil.

She and her two sisters--Fotla and Banba--were the goddesses of the island, and thus each was a poetic name for the island, with "Ériu" the official name. Even today, the Gaelige name of the island is Éire. Ériu and her sisters were also sisters to the three war goddesses collectively known as the Morrigan: Badb, Macha, and Anann.

Curiously, though identified as children of Adam, the sisters are according to the Lebor Gabála "older than Noe... on a peak of a mountain was [Banba] in the Flood." The only two other people which are said to be this old and to have survived the flood are Tuan mac Carill and Fintan mac Bóchra.

The Lebor Gabála also tells of a meeting between each of the sisters and Amergin, bard of the Milesians. His meeting with Ériu takes place at Uisnech, the "center" of Ireland. From each he is inquired as to the invasion's purpose. Each sister gives consent, with the demand that the island be named for her. Each is promised this, but as Ériu seems to make the most effort to support the invasion, she is the one for whom the island is named. Also, when Donn insults her, it is implied that Ériu caused his death by magic.

Her husband was MacGréine, one of the three grandsons of the Dagda. His name means "son of the sun," and the Lebor Gabála claims that the sun was his god--or possibly that he was originally a solar deity. That the land would be married to the sun is not implausible, at least from a mythological standpoint, but it would be unusual.

Ériu, as "Flaith Érenn", is the woman who gives Conn the cup of sovereignty in Baile in Scáil. This episode is likely a reflex of the older ritual described by Michael Enright in Lady with a Mead Cup, wherein the woman acts as prophet and king-maker. In Enright's book, this function is identified with the continental goddess Rosmerta, consort of Mercury. In Ireland, Flaith Érenn is seen seated next to Lugh, who is usually identified with Mercury.

Mother of Bres?
In The Second Battle of Magh Turedh, there is a woman named Eri daughter of Delbaeth who is said to be the mother of Bres, but whether this is the same woman as Ériu is not entirely clear. It's entirely possible that Ériu is meant, which may be one of the reasons Bres is elected to replace Nuadu. On the other hand, the name Delbaeth is given to so many figures in the mythological cycle, it's unclear just which Delbaeth this may be, as Bres' father is also the son of a Delbaeth, and yet the text makes it clear that Eri and Elotha do not know each other.

Etymology
There are two possible etymologies. The first gives descent from Old Irish *Īwer-iū to the Proto-Celtic *f-weryon- "earth, soil", and through that to Proto-Indo-European *peiə- "fat", here used in the sense of "plentiful".

The second etymology derives Ériu from the proto-Celtic *aryo– "free man", from the PIE *h₂eryo- "noble" or possibly "member [of the tribe]". From this is derived the words Aryan and its offshoots, such as Iran. However, this is less likely than the first etymology, as Ériu is shown in earlier documents to Iweriu (or some variation on that name), which does not easily derive from *aryo-. Moreover, the Old Irish word descended from *aryo- was aire, "free man".

The modern version of the name is Éire, which is the proper name of the Republic of Ireland (Poblacht na hÉireann). The dative case of Éire gives us Éirinn, and thus the popular name Erin and the phrase "Erin Go Bragh"

SOURCE
Enright, Michael J. Lady with a Mead Cup: ritual, prophecy, and lordship in the European warband from LaTene to the Viking Age. Dublin: Four Courts, 1996.

Lebor Gabála Érenn: The Book of the Taking of Ireland. Part IV. ed. & trans. R.A. Stewart MacAlister. Irish Texts Society, Vol. XLI. Dublin: The Irish Texts Society, 1941.

"The Second Battle of Magh Turedh". Ancient Irish Tales. ed. & trans. Tom P. Cross and Harris Slover. Dublin: 1936.