How does ice-skating work?
The weight of the body acting on the small area of the skate in contact with ice exerts a pressure sufficient to melt the ice. The water formed lubricates the skate and causes a low coefficient of friction. As the skate moves forward, the pressure is reduced and the water refreezes.
Leaning on one side will increase the friction and give them the ability to manipulate their movement, left or right mainly. Pushing the blade lengthwise into the ice will provide enough friction to push the skater forward at potentially high speeds. A good skater can combine the pushing technique with the leaning technique to obtain a graceful movement called drawing.