Calories (or kcal) is a measure of the energy you've burned during your activity. Strava will calculate calorie data for your rides and runs. Calorie calculations are estimates based on power output and a coefficient for human efficiency.
To get calorie calculations for rides, Strava requires power data. Power can be estimated if you enter your weight and the weight of your bike, or you can use a power meter to get a more accurate measure of your power output. See Power Calculations for more details. If you are having trouble getting your Strava Power to calculate, see How to Get Power Calculated on your Rides.
Calorie calculations for runs require that you enter your weight. Strava will use your weight and the elevation data and distance of your run to estimate calories burned. If you're having trouble getting calories calculated for your Runs, check or reset your elevation correction by following the instructions on Elevation Correction for your Activities. Calories for runs are a function of speed (grade adjusted), weight, and moving time. Multiply these together with a scaling factor, and that's the estimate.
Calorie calculations are only estimates. You may notice differences between Strava's calculations and those from other tools, even given the same activity data. This is most likely due to differences in Calorie calculation algorithms, and the data factored into the calculations. We believe our estimation is as accurate as possible given the limitations in data.