Welsh: The name has a dual connotation:
(intensifying prefix) + dwfn
: deep = "The Very-Deep Place"
(negating prefix) + dwfn
: world = "The Not-World"
A variation on the name Annwn, the Otherworld (northern and southern Welsh variations? I'm not sure). This form occurs in "Pwyll pendeuc Dyfed," while Annwn appears in the (arguably later) Welsh Triads and poetry of Taliesin. Ruled in some texts by Arawn, in others by Gwyn ap Nudd.
Annwfn is generally associated with hills and islands--high points, which, possibly, were originally the burial mounds of the Pre-Celtic and Celtic tribes.
Lloyd Alexander anglicizes it as Annuvin in the Chronicles of Prydain.