A sharp knife cuts better than a dull knife because a sharper edge has less surface area. A smaller surface area will exert more kinetic force in a concentrated area.
A sharp edge on its own does not cut anything; it requires motion to create kinetic energy or force. Generally, a person's hand pushing or pulling on the handle or the back of a knife provides the kinetic force. When a knife is dull, its edge has more surface area, so the exerted force is spread out over a larger area. In other words, there is less to go around in any given space on the edge. When the knife is very sharp, the force is concentrated into a very small surface area and is more able to push through whatever is being cut.