Vaping is simply a new way of enjoying the sensation you get from using nicotine.
Instead of burning tobacco leaves and inhaling the resulting smoke, you heat up a liquid infused with pharmaceutical nicotine (this is extracted from tobacco) and flavours.
When heated up using an e-cigarette, this, in turn produces vapour, hence the phrase vaping.
Generally a vaping device consists of a mouthpiece, a battery, a cartridge for containing the e-liquid or e-juice, and a heating component for the device that is powered by a battery.
When the device is used, the battery heats up the heating component, which turns the contents of the e-liquid into vapour that is inhaled and then exhaled.