When a piece of metal has been tempered into two or more different Rockwell hardnesses. This was the historical method of making katanas. During the tempering process, clay was placed over the back of the blade, keeping most of the heat out and keeping it relatively soft, around a Rockwell 20-30. The edge was tempered to a Rockwell of the high 50's/low 60's. This meant that the edge was very tough and would hold an incredibly sharp edge for a long time, but the back of the blade was flexible enough to keep the sword from shattering. The differential temper is actually visible in the temper line, or hamon, that runs the length of the blade. Most katanas made today are not differentially tempered and have a false hamon, though real ones can be had for prices ranging around $550.