The name is of Icelandic origin and in English it means something like "The black castle" or "The dark fortress¨.
(Quote frome an interview with DB)
'Cataclysm Children' (English)
'Allehelgens Dod I Helveds Rike' (Norwegian...if you can't tell)
Sure, they're not traditional black metal like bands such as Bathory or Emperor, and their lyrics can be somewhat.. crazy.. but the music is intense and awesome.
So, before all of you start yelling at me and calling me some sort of evil goth Satan-worshipper.. first of all, I'm Christian and I don't worship Satan, and second of all, I'm not trying to relate to their lyrics - I just like their music. If I wanted to find some good meaning in lyrics, I'd look at bands like Stratovarius or HIM, both of which are also really good.
So once again, Dimmu Borgir is an awesome band, and for those of you who want some nice heavy metal, I suggest checking these guys out.