Plasma cutters work by sending an electric arc through a gas that is passing through a constricted opening.  The gas can be shop air, nitrogen, argon, oxygen. etc.
 
This elevates the temperature of the gas to the point that it enters a 4th state of matter.  We all are familiar with the first three: i.e., solid, liquid, and gas.   Scientists call this additional state plasma.  As the metal being cut is part of the  circuit, the electrical conductivity of the plasma causes the arc to transfer to the work. 
 
The restricted opening (nozzle) the gas passes through causes it to sqeeze by at a high speed, like air passing through a venturi in a carburetor.  This high speed gas cuts through the molten metal.  The gas is also directed around the perimeter of the cutting area to shield the cut.