I think it might be a strap to hold down one of those big U-shaped locks like you see for bicycles.
Whats a U lock? what feature do the european bikes have? my insurance papers are under the rubber strap on the seat
I used it to hold some of my loose wires that for my Fender Eliminator.
I would suggest not to keep any documents dhere unless you want to get them wet in the rain :-/
Its not a waterproof compartment