You make the edge of the metal as fine as possible.
By doing so, you decrease the area of the edge of the blade which in turn increases the pressure.
A blunt blade has a large surface area on the edge of the knife, a sharpened blade has a small surface area on the edge of the blade.
Pressure = Force / Area
Now in both cases, force can be the same. But the smaller the area value the higher the pressure.
Example (numbers exaggerated):
Let's say you have a knife that is blunt. The area of the blunt edge is 20cm2. You apply 100N of force. This gives a pressure of 100/20 = 5N/m2.
Now you sharpen it, the area reduces to 5cm2. You apply 100N of force again. This time you have a pressure of 100/5 = 20N/m2.
Basically, you are removing atoms from the material with each pass.