Vape Batteries come in all shapes and sizes
Depending on what kind of vaping you're going to be doing, you're likely to have one of a variety of different types of batteries. From cigalikes that mimic the shape and size of an actual cigarette to mods that are larger than a pack of cigarettes, navigating the world of what different kinds of batteries are good for what can seem complicated, but it's actually not as complicated as it looks.
The first (and oldest!) of all "vape" batteries is the cigalike. They come in many colors and styles, but they share the fact that they're thin tubes that mimic a cigarette. There's been research suggesting that they are the least efficient of all ENDs (Electronic Nicotine Delivery Systems). They typically are composed of a small battery and a cartomizer that screws on that is roughly the shape and size of a cigarette filter. This cartomizer is pre filled with e-liquid in a particular flavor and nicotine level and is a consumable, meaning that rather than buying a bottle of e-liquid, you typically buy cartomizers. Some brands do make "refillable" cartomizers, but they typically function poorly and can only be refilled a limited number of times.
The 18650 is one of the true staples of vaping that has stood the test of time. It is also the culprit behind many of the gigantic "mods" some vapers prefer. These batteries are about half again as large as a AA battery, and they pack a serious punch. Originally (and still) used as power cells for electronic items like video cameras and laptop computers, they've found a perfect place powering e-cig devices. The 18650 is typically charged separately from the device that it powers, meaning they typically require an extra piece of equipment, a charger! These chargers range in style and price, but the best ones are developed to specifically charge batteries at a low, stable current, unlike how you tend to charge most of today's electronics. Using them safely is very important as they are true power cells and can short out, causing everything from a very, very hot battery to a smoldering chemical pile and melted vape mod. While the latter is uncommon, it is the reason battery safety is critical.
The "EVOD Style" Battery
Often called a stick or pen battery, these are simple tube shaped batteries that come in a wide variety of lengths, colors, widths and more. They typically feature an eGo style connector and a simple button mechanism for firing. Some have the ability to vary voltage within a minimal range or charge with a USB cord, but they typically require a special charger in order to charge them.
How it all fits together
E-cigarettes are digital devices. They use modern technology (and a lot of not so modern basic electrical principles) to apply power to a heating element. Your battery is the thing that provides that power, and your atomizer is the vehicle that transforms that power into the heat your E-Liquid needs to create vapor. It's actually a very simple system, mechanically, but the beauty of vaping is that batteries and atomizers can take an unbelievable range of shapes and forms. Some of these are specifically designed to operate using digital chips to control voltage and amperage output (therefore temperature), and some are just raw tubes throwing every bit of power straight at your atomizer. Whatever the case, your battery functions as an integral piece of your e-cig and is critical to your overall vaping experience. Having good quality batteries is a must if you take vaping seriously, and you'll thank yourself for buying good ones and keeping them in good condition.