R. I. Thomson glosses Annwfn as An Dwuyn “fearfully deep”; “the not (this) world” (PPD p. 25–26 n. 44). Patrick Sims-Williams summarizes the possible etymologies for Annwfn as follows:
Patrick Sims-Williams said:
The term annwfn was doubtless understood as intensive an- plus dwfn ‘deep’ (cf anoddyn ‘abyss’ <an- + *wo- ‘under’ + dwfn), and this may indeed be the correct etymology, as Eric Hamp has noted. . . . Ifor Williams . . . suggested that the second element might be dwfn ‘world’(cf. Gaulish dubno-, dumno-) . . . With dwfn ‘world’ as the second element, the first could be an- < *n- ‘not’, hence ‘Not-World’ (Sims-Williams 1990, 62)
It is important to note that Annwfn is very much a different world; though it appears disconcertingly easy to pass from Wales into Annwfn, even crossing without being aware of it, it is a separate world, with its own kingdoms, rulers, peoples, and customs.
