A crossover is a technique used to change direction while maintaining speed. In a non-crossover turn, the inside skate essentially glides around the turn while the outside skate does several pushes. This is inefficient because only half as many pushes are being made. In a crossover, the outer skate does a normal push ending on the inside edge of the wheels, however, the inside skate instead of gliding does an "underpush" starting and ending on the outside edge of the wheels with the inside foot on the other side of the body's midline just slightly behind the outer leg. Then just before you're going to fall over, the outside leg crosses over the underpushing inside leg breaking the fall and starting the normal push of the outside skate. In this way the crossover is a continuous powered falling motion around the corner with the skater held up by the centrifugal force of the turn. Crossovers done correctly will also allow you to accelerate hard out of turns. It's pretty easy to do a generic crossover, but very hard to get the motion to be fluidly efficient.