If you have a look in the settings it gives you an idea of what your body burns on a normal day, without exercise etc. The total that MFP gives you as a goal to eat is based on no added exercise. This means in order function properly during the day, whilst still eating at a deficit, you must eat "blah" amount.
As soon as you add exercise, You are burning more than what your body has to store. You eat back (most) of your exercise calories because otherwise there isn't anything left in the tank to burn.
Burtle has it right.
There is a limit though. You shouldn't really go below 1000-1200 a day because your body starts to slow down other processes and store energy, so effectively your metabolism doesn't work as hard as it normally does.
If you don't want to eat back your exercise calories and you aren't hungry then don't. Just be aware that if you are starving after you exercise and your body hurts more than normal, it's not getting enough fuel.
I personally use mfp, runkeeper and have a fitbit. I find my fitbit is a far more accurate calculator of what I'm burning everyday.
Even just reading about various fitness tools like those, give you more of an idea how bodies work.
Either way, listen to your body, not your head. You'll soon realise if you are actually hungry or thirsty, or bored.
And eating way less calories to start will make you drop quickly. But as I said, at some point it will just stop and start conserving instead of letting you lose.