There are different types of water heaters, and a power vent water heater is just one type of the two. The old and traditional water heaters used something called a natural draft water heater. These types of water heaters would use pipe called "flues" and the gases would rise up through the flue and out of the chimney.
Now in modern times we have some called the "power vent" and you will now see power vent water heaters being installed in many places. Now lets get to how they are different. A power vent water heater has a blower motor that will "blow" or "force the emissions" through pipe allowing you to vent the water heater a way further difference then a normal or standard water heater.
So with that said, The reason you would need a power vent water heater is if you did not have a chimney or a stack to vent the regular type of hot water heater. A good example of this would be an addition to a home, or maybe even replacement of the old water to a different location.