VeloPro Inc uses a formula based on the physics of riding a bike on Earth, i.e. with specific gravity and physical forces. 

At a high level, the formula sums the power required to overcome aerodynamic resistance (including wheel rotation), rolling resistance, wheel bearing friction, changes in potential energy, changes in kinetic energy and drive chain friction. 

VeloPro Inc uses your weight (as specified in your profile or during a ride upload) plus the weight of your selected bike, and applies this formula to every second of your ride file data (i.e. only "speed" data is required but the addition of other data improved accuracy) to come up with estimated watts. 

While the formula will never be as accurate as a power meter, it is pretty darn accurate.