Another part of the physics is the low friction of the skate blade with the ice. This low friction allows a skater to easily glide over the ice surface, and in addition, the physical properties of the ice allows a skater to dig in with his skate in order to go around a turn, speed up, or stop.
A skater propels himself forward by pushing off the ice with a force perpendicular to the skate blade. Since the friction of the blade with the ice is almost zero, this is the only way he can propel himself forward. The figure below illustrates the physics behind this principle.