How is this any different from drip coffee? Drip coffee passes though the grounds very quickly, going through a paper filter. The AeroPress has a paper filter as well, and so it would seem that the coffee would pass through the filter by gravity alone.
If the press speeds up the process of passing through the filter, then it would seem you'd need a lot more grounds to compensate for the short brewing time.
The finer grind you'll use allows a shorter brewing time. Using a finer grind is possible because of the denser filter. The pressure of forcing the water thru the filter adjusts the brewing time (that, and the stir time). The shorter contact with the hot water means a smoother brew, less acid, less sour stomach for coffee lovers. You can also experiment with the stronger coffee flavors even if you do like medium strength coffee, because of the smoothness of the aeropress system and the ease in which you can adjust the coffee to your tastes.
The Aeropress paper filter provides a good deal of resistance, requiring more pressure than gravity. But contrary to espresso it is recommended that you use a lower temperature water, about 175F. The low temperature, high pressure extraction provides consistently better coffee than the high temperature, low pressure drip machines I have used.
They have a good video on their website outlining the whole process. Having used home espresso machines, drip machines, and a French press I'd highly recommend getting the Aeropress.
The Aeropress uses a combination of pressure and steeping the grounds. You pretty much make "espresso" with this machine. This product produces crema, which is kind of like a nice froth. The process takes about a minute once you have hot water. So, making one shot of "espresso" or one cup of coffee Americano takes about 1 minute. The end product is not quite like a french press, not quite espresso (but very close if not superior-kind of like espresso without the gross aftertaste), and not quite coffee Americano. I would not recommend this to make more than 2 shots of "espresso" at a time. So, if you need a lot of coffee, stick with a coffee maker. If you want a quick cup or two of coffee, espresso, or latte, this is a fantastic device. The "coffee syrup" you produce refrigerates pretty well if you are like me and want a quick latte to start the day. 1 shot of espresso, one cup of Silk lite chocolate soy milk and instant joy.
It does use quite a bit more coffee. However, I'm told the best flavor from coffee is extracted from the grounds when they are first extracted from the hot water. A drip passes water over the same grounds for quite a while and can over extract the coffee. Pulling other flavors from the coffee. I've had the aeropress for quite a while and the coffee it makes is very good. I usually make a double, then double the amount of coffee it makes with hot water. The paper filters are very fine, it would take forever for the water to 'drip' through the aeropress.
You have more control over brew time and water temperature with the Aeropress and using the inverted method. With drip coffee, brew time and water temperature are dependent upon the coffee machine you are using. The Aeropress allows you to experiment with these two variables; and I think the optimal combination of brew time and water temperature varies with the coffee grounds you select to use.