External Battery Power for Phones, Laptops, Etc.
Portable Power Solutions
External battery power is most often used for notebook and laptop computers. This is because the included batteries are usually limited to a few hours of life, given the manufacturer's need to shrink the entire case. As you may have already discovered, the Lithium Ion battery constitutes the bulk of the computer's weight, so smaller batteries usually give you less power life.
However, external battery power is not just for computers. Handheld devices have very limited battery life, so backup power is usually a great idea if you're going anywhere without power readily available. If you have a digital camera, MP3 player, Iphone, or camcorder, you might want more power than you are getting right now, especially for heavy use and professional grade audiovisual purposes. It is even possible to use a USB cord to backup power on some smaller devices.
At the large end of the scale, external batteries are even used for homes. If you're relying on solar power, you need something to capture that energy for times that the sun is behind clouds or on the other side of the Earth. There are very big capacity batteries and capacitors for this very purpose.
Few people seem to consider that the original use for external batteries in the computer world was (an still is) for desktop computers and servers. UPS backup is great for surge prevention and for keeping your systems running when the power goes out. For mission critical data, a battery backup saves time, prevents losses, and protects you long enough to create a data backup.
Notes and Special Information
Special note: External battery power needs to be compatible with your voltage requirements and polarity. Don't buy cheap external batteries or else you may end up with battery leakage or detonation.