All e-cigs, vapes and mods are powered by batteries, either built-in or user replacable. The naming scheme of the battery refers to its physical dimensions, an 18650 has an 18mm diameter and is 65mm in height, the 0 refers to its shape which is cylindrical. To use another example, a 21700 battery has a 21mm diameter and is 70mm in height, again, the 0 refers to its shape which is cylindrical. The most common type of batteries used for vapes are 18650's but some take for example a smaller 18350 or a larger 21700.
All batteries of this type have technical specifications which are important to be aware of. It has a rated capacity (mAh), and a current rating (Ampere, A). To learn more about which battery to choose, click here. If you want to know how long they take to charge, click here.