Arduino is pretty universal development board. It can accept power supply from several sources including USB, DC jack that is followed by linear regulator, or simply it can be powered directly with 5V (or 3.3V in other boards). If you want to power Arduino as portable devices or remote device where is no power lines, then the only logical option is to use battery based power supply with efficient regulation. Of course you could use like 9V battery and then plug in to DC jack, but this is very inefficient, because almost half of energy is wasted as heat. So you need efficient step up regulator which would boost voltage to required 5V without much loss.
Artificial Intelligence shared an instructable where he shows a simple way of powering Arduino from battery pack made of two AA batteries. He constructed a simple Arduino shield that sits under Arduino board. As you may know two series AA batteries give 2.4V or 3V if not rechargeable. A simple step-up circuit made of MAX756 boosts voltage to 5V. This way is much better than powering board from 3 series AA. Because this is not regulated and there is a risk of supplying to high or too low voltage. Also boost regulator helps to drain battery without affecting supply voltage.