It all comes down to how many augers and impellers the snow thrower has. A single stage has a single auger, while a two-stage has augers and an impeller, and a three-stage will feature augers and two impellers.
The more impellers a model has, the more snow it can clear, and faster. A single-stage model may only be able to clear dry, powdery snow up to just 6 inches deep since its single auger acts like a scoop; picking up snow and throwing it through the chute and out of the way. It doesn’t have a lot of power on its own, so a single-stage snow thrower may only be able to eject snow up to 20 feet away from the operator. This means you run a higher risk of having snow blow back into your clearing path or all over you. A two-stage model uses a pair of front augers to break up snow drifts and feed debris into the impeller, which accelerates snow and small ice chunks through the chute, up to 40 feet away from the operator.
A three-stage snow thrower can handle wet, heavy snow up to 2 feet deep, and even thin layers of ice that may have formed from melting and re-freezing snow or sleet. This is because the side augers feed snow and ice into the center impeller (also known as the fan-auger), which helps break up big chunks as well as accelerate debris into the final impeller, which accelerates debris even further to throw snow up to 60-feet away from you (depending on the model).