It's means where a river meets the sea i.e Abertawe is where the Tawe river meets the sea. (Kind of like Estuary but we have another word for that).
According to Wikipedia, it's not Swan-sea but Swans-ea and may come from a Norse name -- something like Sveinn's island or Sveinn's inlet. Possibly relating to the Danish king Sweyn Forkbeard.
So the -ea ending may be the same as the -ey of placenames such as Anglesey or Orkney.
Sveinsey. Svein's island (would be spellt "Sveins øy" in modern Norwegian).
There's an island in Swansea bay giving it's name to the whole area.
It's the exact equivalent of 'mouth' in English city names, eg Bournmouth, Avonmouth, Plymouth etc. It is very common as a place name in Wales, we have a lot of rivers :-)