For Rush, I feel like I have a pretty good grasp on their history, the major points of interest, from reading books and essays and all those sorts of things. Then Beyond The Lighted Stage came out and I was BLOWN away, but it helped me reaffirm my love for the band and realize that I really did know a lot about them, but there was still more to learn.
As for other bands, like DT, Yes, Genesis, Marillion, Spock's Beard, The Flower Kings, Porcupine Tree... I know all their albums, the members on them, what they played for the most part. I try to get a good history on every band I love, not to try and be a knowledgeable show-off, but just to basically understand MORE about the music itself. If I like a song or an album, I want to know what the band's influences were then, what they did, what their techniques were (especially drummers), etc. etc. It helps me understand the music more if I understand the musicians behind it.
-Marc.