Please Help Me Understand!

Eating more food won't decrease your deficit. Your deficit is already built into the MFP system. If you are given 1200 calories for the day and you are trying to lose 1 pound a week, that means your body burns 1700 calories a day before exercise. When you exercise you are burning more calories than usual so you need to eat to make up the difference and keep the same deficit. In addition, it's important to give your body the fuel it needs to work out, so if your deficit is too low from not eating enough, you can hurt your body.

From what I have read the mfp calorie counter already has the deficit regardless of whether you exercise or not. By exercising you are increasing that deficit to sometimes unhealthy proportions. I personally eat back my calories which sometimes means I eat over 3000 calories a day! But as long as I keep to my net goal I still lose weight.

Exactly... presuming you've already set the MFP Tools that you want to lose say 1.5 lb per week, the caloric goal set for you has already reduced the amount of calories from your BMR (Calories you burn by being alive, everyday normal behaviors) usually it's about a 200 cal reduction, but this can vary. The excercise helps your body to speed up the metabolic rate, build muscle (which burns fat, and endurance and a basically whole better you) so while you can literally lose weight just cutting the calories MFP has taken from your BMR it is best to couple it with exercise, which burns more calories, but requires you to "eat back" just like filling up the tank of a car... required energy. If you hadn't already reduced your calories ie) your BMR is 1650 and you want to eat your face off all the time and haven't cut your calories down to say 1450 and you continue to eat 1650 calories per day, if you exercise and burn 200 calories per day you would still lose the weight. Long story short, if you've cut calories and are following MFP reduced calorie goal then eat back your exercise calories (at least most) and if you aren't following any MFP reduction in calorie goal, then don't eat back your calories.
Cheers,