Alright friend, get ready for a tiny science lesson.
So the human body basically works in a way that's very similar to a car. Calories are just a unit of energy. Think of them like the gas that you put in your car. Now, when you turn your car engine on, that's your car being alive. It's burning the gas in the tank, whether you're actually moving or not. You'll burn more gas the faster you're moving, but as long as your engine is on, you're going to be burning fuel.
The same thing goes for your body. Your body burns calories as long as you're alive. It needs this energy to fuel your engine-- your heart, lungs, brain, and everything else. If you start moving, you burn more calories. And if you're moving really fast, you burn even more. Which is why people exercise when they want to lose weight. They're moving more to burn more fuel.
Most people who are average-sized adults need to eat at least 1000 calories to fuel their basic life functions. That means that even if you slept through an entire day, you would still burn 1000 calories just by being alive. You said that you ate 1050 calories. If we say that your basic life function (metabolism) required 1050 calories to run, you burned an additional 1034 calories through your daily activity. That's like trying to drive 200 miles on 100 miles-worth of gas. A car physically can't do that. The human body can because it will burn fat stores instead of the food in your belly.
You're probably thinking, "but my goal is to burn fat, so if I use more calories and eat less, that's good, right?" Well, yes, to a certain point. You have to have a calorie deficit in order to lose weight. But in the same way that a car doesn't work without gas in it, your body will start to not work.
People call this "starvation mode." It's your body's way of ensuring that you will continue to survive. Your body has a mind of its own, and it's assuming that because you're not feeding it properly, there must be no food around to eat. When your body thinks that there's no food, it adjusts its metabolism (the rate at which it burns fuel) in order to prolong the use that it can get out of the little amount of food that you do eat. One of these metabolic mechanisms is fat storage. If you eat a larger amount of food than normal, your body will hold on to every precious calorie that it can in the form of fat to save for later. If you continue to not eat enough, and your body depletes all of its fat stores, it will begin to break down your muscles to use as energy. Which is why starving people look like "skin and bones."
NOW, in the short term, you're right, eating a lot less and burning a lot more will cause you to lose a lot of weight, but that kind of weight loss is not sustainable. If you reach your goal of losing twenty pounds and start to eat more again you're going to gain a lot of weight in the form of fat, because your body was used to starving and wants to keep itself from starving again. If you reach your goal and don't increase your intake, you'll continue to lose weight until your body starts to break down its own muscle for food. Then it will attack your vital organs and you will have some serious health complications associated with starvation.
The best way to go about losing weight is to have a SMALL deficit. Your calorie deficit is about 1000 calories. You should probably have a much smaller deficit of 200-500 calories. Your weight loss will take longer, but if you continue to exercise and increase your intake to equal your burn rate after you've lost the 20 lbs, you'll be in good shape and hopefully will neither lose nor gain weight.
