Simply put, vape batteries are the heart of your vaping experience. Without going into unnecessary details, they store and release the power that the atomizer uses to transform vape juice into glorious clouds of vapor. 
This component isn’t the same across all vape units. There are variations in terms of type, capacity, and configuration, although this might be a detail that would concern the more hard-core vapers. 
The most important thing, and the one that you absolutely must remember, is this: Without charge in your vape batteries, you won’t be able to vape.