Why do we use Lithium Ion batteries?
The main reason Lithium-Ion batteries are used for LED torches, is that they have a high 'energy density'. This just means they have a lot of power in a small size.
A typical 186560 cell is rated at 4.2V (Volts) and 2800mAH (milli-Amp Hours), in comparison an alkaline AA battery is 1.5V and only 2000mAH. This means you would need 3 cells and then the capacity would be lower.
Another benefit of Lithium Ion cells is they can deliver many times their rated current; this us useful as LED`s draw a lot of power when first turned on.