Independent energy sources for portable devices have always been a matter of research and discussion. It all depends on the particular application the source will be used in. Requirements will not be the same for motors, lighting, whether stationary or mobile, low current drain devices, appliances permanently ON or frequently switched ON-OFF, etc.
For use in flashlights, it appears that the most desirable features of 18650 batteries are the energy density that can be stored, the capacity of outputting high current, the size and weight.
Before flashlights adopted them, 18650 battery cells were industrial parts mostly used as components making up larger battery assemblies. Then flashlight manufacturers adopted them in view of their characteristics which make them very suitable for that particular use.
These batteries are called 18650 because of their dimensions: 18.6 mm in diameter* 65.2mm in length. This style of denomination has become a sort of standard in the industry. For example, we can find 14500 cells, the size of an AA alkaline battery. But watch out: some brands are slightly bigger than others with the same denomination so you’d better check for compatibility with your flashlight before investing your money.
Polymer Lithium ion Batteries are lithium so they pack extremely high energy density. Output voltages vary from 3.7V to 4.2V and the power to weight and size ratio is better than with other technologies. They usually have a very low self-discharge rate and no memory effect. 18650s usually can be recharged up to 600-1000 times, depending on the brand. Due to their chemical content, batteries in general are potentially dangerous parts. Usually, any 18650 battery has a protection against over temperature and over pressure.
There was a time when 18650 cells were reputed to be prone to explode but this was changed with the addition of a Protective Circuit Board. Such batteries are called Protected 18650s. The PCB is inserted at the bottom of the cell. The protection works against over current, over charge and over discharge. A protected Nimh battery is slightly longer and bigger than an unprotected one. They should be named by the proper designation: 19670, although for historic reasons, most people including manufacturers keep using the incorrect designation: protected 18650.