Am I to understand = let me get this straight = let me make sure I understand = I want to be clear, what you are saying is ...

"So, what you're saying is _______" "Am I to understand ______?" just sounds more formal. It sounds like what a teacher would say to you when you're in trouble. I think I can go into more detail if you'd like, but that's the gist of it.

It's an expressive way to say "As far as I understand..."