Ultimate small size mobile DSO!

Forgive me for going off topic a bit, but, once again I will be showing my true colors (i.e. revealing that I'm a software person, and not an electronics-hardware person) by asking a simple question I can't wrap my head around.

Will someone please explain the functional difference between a digital scope and an analog one? Why can this digital scope cost so little, when it seems like even a low quality analog scope is a few hundred $$?