Adding to what Steve said:
When you bottle, the carbonation level is determined by the amount of sugars you give the yeast to consume. The end result will be a finite amount of CO2 contained within the bottle. Some of this CO2 is absorbed into the beer and some remains in the head space. Theoretically, this state of equilibrium will remain the same until the bottle is opened. Once the bottle is opened, the CO2 in the head space will be lost. If you were to recap the bottle immediately, the beer would release some of the CO2 it has absorbed into the headspace in order to again reach equilibrium, resulting in a lower carbonation level.
Five gallons of beer in a keg will yield 40, pint servings. Each time a pint is drawn, the head space in the keg is increased by the volume of a pint. Without a regulated supply of CO2, a process very like that in the bottle example above, would occur with each pour. Each serving would have a lower carbonation level than the previous one until the beer remaining in the keg was almost flat and there was no longer enough pressure to move the beer from the keg through the faucet and into the glass. Serving pressure is the pressure it takes to produce and maintain the desired carbonation level. With this pressure applied constantly the beer doesn't need to release any CO2, so the carbonation level theoretically remains the same from the first pint to the last.
