Damnably is a strong way of saying very — but only when the thing is bad, unfair, or enough to make you swear a little, at least inside your head. It is an adverb, so it usually sits in front of an adjective or a verb: damnably hot, damnably unfair, he behaved damnably. Underneath it is the old religious idea of damnation, of being sent to hell; though actually, almost nobody who says it today is talking about God. They are just turning the volume up on a complaint. The word sounds a little old, a little bookish, and a little British. In ordinary talk people are more likely to say damn, terribly, or ridiculously. You will still meet it in novels, and in the speech of people who like a colourful word.