Your BMR, when you find it (more on that later), is basically how many calories your body burns if you were to stay in bed all day; exercise and things are additional calories burned.
In other words, if your BMR is 1800, and you burn 700 calories in a workout, in theory, you've burned 2500 that day.
That being said, finding your BMR is going to take experimentation. Websites (like Traineo) can give you a rough estimate, but your actual BMR is based on a lot of factors that you can't really easily measure on a website (lean body mass, etc.) Muscle burns calories just existing in your body while fat doesn't, so a 200lb guy at 30% body fat is going to most likely have a significantly lower BMR than a 200lb guy at 10%... make sense? It's going to take experimentation to find your magic number of how much you need to eat to not be hungry, as opposed to eating until you're stuffed.
I would also caution against being too calorie focused. You definitely want to keep track of what you eat, but it is only one small part of the whole process, and people who focus too much on calories in and calories out have a tendency to cut back too harshly on their bodies calorie needs which is dangerous and detrimental to the overall goal of being healthy.
The most important thing though is that you should never actually be hungry; hunger is a sign from your body that you should not ignore, but if you're like most people these days, you're used to stuffing yourself until you're beyond full, so you'll basically have to relearn how to eat so you can relearn your bodies signals. Too many people try to force themselves to ignore their stomach when it rumbles, and that's just as bad, if not worse, than eating until you can't move...
