"Plain of Apples"
The home of Manannán mac Lír and one of the names for the Otherworld. The name is cognate with Avalon.
A branch of the apple-tree from Emain
I bring, like those one knows;
Twigs of white silver are on it,
Crystal brows with blossoms.
~~The Voyage of Bran~~
Emhain Abhlach is one of the many names of the home of Manannán mac Lír, god of both the sea and of the Otherworld islands. While the Tuatha Dé Danann live in the Hollow Hills or sidhe of Ireland, Manannán's realm is the Blessed Isles beyond the sea, reachable only by the chosen. The chosen are usually those who the daughters of Manannán have fallen in love with, such as Connla or Oisin. Other chosen ones are Bran and Cormac mac Airt, the later of whom was specifically brought in order to claim the sovreignty of Ireland and legitimize his reign. For those who unwisely leave Emhain Abhlach, the return to this world is a shock, brought about by the realization that hundreds of years have passed, while to the hero it seemed only a few days or years.
The symbol of Emhain Abhlach is, of course, an apple, but more importantly, a golden (sometimes silver) branch of apples carried by either a youth (Manannán in disguise) or a young woman (one of Manannán's daughters). This branch, when shaken, made music which healed the sick, relieved all care, and brought deep sleep.
On Emhain Abhlach, Manannán raised Lugh Lamhfada until the Second Battle of Magh Turedh. The idea of raising a hero on an Otherworld Island is not uncommon in Celtic myth; it is also seen in the story of Lugh's son, Cuchulainn, raise on the Isle of Skye.
'Without grief, without sorrow, without death,
Without any sickness, without debility,
That is the sign of Emain--
Uncommon is an equal marvel.
It is a paradise, free of the warfare of the sidhe, which, while being the home of the gods, is still a dangerous land to visit. Perhapse this is because the gods still live on the land, still live close to man. Perhapse the remoteness of Emhain Abhlach promotes its peaceful manner. This description draws a parallel with the Arthurian Avalon (from afal, "apple"?), where there is peace, healing, and eternal life.
There is some speculation that Emhain Abhlach can, to some extent, be identified with the Isle of Man. However, while Manannán mac Lír is associated with both places, this would seem a later euhemerization, attempting to rationalize the myths with a Christianized worldview. Moreover, this wouldn't make much sense, as the Otherworld islands are held to be out in the west, while the Isle of Man is east of Ireland.
While some say that Emhain Abhlach is a land of the dead, or possibly an Irish Valhalla, this is not quite the case. Though it seems that some few, lucky souls do reach these islands, the majority of humanity, according to the druids, are destined for reincarnation; even the gods experience reincarnation, instead of automatically residing on the Otherworld Islands. Emhain Abhlach is extremely difficult to reach, and it seems that no personal attempts will bring one there; only being chosen by Manannán for his own reasons.