BMR, TDEE and your target
Your basal metabolic rate (BMR) is the energy your body uses at complete rest. The calculator uses the Mifflin-St Jeor equation by default, which studies found to be the most accurate of the common formulas for most adults: 10 × weight in kg + 6.25 × height in cm - 5 × age, plus 5 for men or minus 161 for women. A 30 year old man of 180 cm and 80 kg has a BMR of 1,780 kcal. The revised Harris-Benedict equation (Roza and Shizgal, 1984) is available as an alternative and usually gives a slightly higher number.
Total daily energy expenditure (TDEE) is BMR multiplied by an activity factor, from 1.2 for a desk job with no exercise to 1.9 for hard physical work or training twice a day. This is your maintenance level: eating about that much keeps your weight stable.
Losing or gaining weight sensibly
A deficit of 500 kcal a day leads to roughly 0.45 kg (1 lb) of weight loss per week, since about 7,700 kcal equal one kilogram of body fat; 250 kcal gives half of that. The same amounts above maintenance lead to slow weight gain, which limits fat gain when building muscle. Real results vary: water weight changes quickly at first, and the body adapts as weight changes, so recalculate every few kilograms.
The macro split turns the target into grams of protein, carbohydrates and fat. Protein and carbohydrates have 4 kcal per gram and fat 9 kcal. The options are starting points, not rules; people with diabetes, kidney disease or other conditions, and anyone pregnant or breastfeeding, should follow their doctor's advice.