To initiate and sustain combustion, three things are needed: fuel, oxygen, and heat. These three components make up what is known as the fire triangle. Each type of fuel has an ignition temperature, which is the threshold temperature at which that fuel can rapidly unite with oxygen.
Above, two of the three components of the fire triangle are available. All that is needed to light the match is heat.
Dragging the match across the rough surface will generate heat due to friction. If the match moves fast enough, friction will generate enough heat and the match will ignite.