Even though this is obviously a German word, I have seen it used in English. I am not absolutely positive what it means, and none of my current dictionaries have it. Could someone help me with the exact meaning?

Dasein is a philosophical concept. You've seen it in English because it's been codified (as much of Freud should have been) in German - there's really no good translation. I believe it was Heidegger who coined the term in his treatise, Being and Time. Dasein ("being there") is the condition of the concretely existing human vis-a-vis his world. It's complicated. It's existentialist. I don't much get it myself.