In the simplest of terms, "Vaping" is a modern form of smoking. Vapers inhale a nicotine-infused vapour from "e juice" or "e liquid". The e liquid is heated by an electronic device, creating the vapour which the user then inhales. Vape devices come in different styles, sizes and formats, including e-cigs and mods.
There are essentially two types of vaping 'style'. The style that you choose to go with will impact which type of kit you need to buy. However, classic or 'mouth-to-lung (MTL)' is usually the best place to start for beginners.