burn 1000 calories

So to lose 2 pounds a week you need to burn 1000 calories a day?
Or is it burn 500 a day, and then have a caloric deficite of 500 a day?

It depends on your current weight, and how much muscle you have.

Either burn 1000 calories or burn 500 calories and eat 500 calories less than your body requires to maintain your current weight

In very general terms, it's either really.

You need a 1000 calorie a day deficit to lose 2lbs of weight a week. Yes, this is highly simplified, but a good way to view it. A lb of fat it 3500 calories, so you need to have a 3500 calorie deficit in order to lose a lb. That would be a 500 calorie a day deficit (500x7).

A deficit can be achieved by either increasing activity, or decreasing food. Don't decrease your food too much or you screw with your metabolism though, because your body needs a certain number of calories to function.

You can look up a few places online where they give you (based on activity, weight, height, age, and sex) the number of calories your body needs a day if you do NOTHING. Then add to that exercise, and subtract what you eat from that. A 1000 calorie deficit should net you about a 2lb loss a week.

There are of course other issues, like bloating, hormones, muscle development, that can alter that a bit, but it's a good base understanding.