Calorie calculators calculate how many calories you need to consume to remain the same weight. If you are active it means you burn more calories during the day, thus you need to consume more calories to remain the same weight. If you'd like to lose weight you should eat less calories then what is recommended (not substantially though).
The key point here is 'you need to consume more Calories to remain the same weight.' To lose weight you need to eat less than that number. The technical term for this is called your 'caloric expenditure' or 'energy expenditure'. What it means is, to lose weight you need to be eating fewer Calories than your 'energy expenditure'.
Generally, one pound of stored fat is equal to about 3500 kcal (or 1kg is ~7000kcal).
As an example. Lets say your 'energy expenditure' is 2000 kcal and you consume exactly 2000 kcal a day (Ie, you neither gain/lose weight). Then you start doing a moderate workout that increases your caloric expenditure to 3000 kcal a day but maintain the same diet. How much body fat mass should you expect to lose in a week?
Well, since you're burning 1000 kcal more than your eating:
(days * (caloric intake - energy expenditure)) / 3500 = lbs of fat burned/week
(7 * (2000 - 3000)) / 3500 = 2 lbs of fat/week
This is an over-simplification because as you gain more muscle mass your caloric expenditure will go up even if you aren't working out and not all exercises are equal but, that's the gist.
For more specifics on setting goals to lose weight without negatively impacting health be sure to take a look at 'What is a Reasonable Rate of Weight Loss to Work Towards'.
Here are some links about what exactly 'caloric expenditure' and 'energy expenditure' define.
Here's a table that shows the caloric expenditures for different types of activities.