It's a nylon briefcase with a shoulder strap. What makes it a bike briefcase is that it loops over the top tube and is held in place by snapping to the bottom and seat tube.
After years of faithful service it is starting to wear out; and I would like to replace it. The brand is "bike brief"; but Google has never heard it, at least the bicycle version. It thinks it's underwear.
I swear I just saw someone post a picture of this kind of setup within the last month here on BF. I think it might have been the guy whostarted three threads to ask about what kind of bags people use to commute to work, but I'm not sure.