Your standard fuel is made of straight and branched, shortish (5-12) hydrocarbons. Long chain hydrocarbons have a high octane rating, and short ones have a low octane rating. Other products, such as cyclic hydrocarbons and benzene may be present, and will have higher octane ratings.
The problem with low octane fuel is that it often spontaneously ignites under pressure at high temperatures (like those in an engine). Now, the engine works by pumping a small amount of fuel into a cylinder, compressing that fuel, then igniting it (with some source of ignition). However, if your fuel is too low quality for the engine you are using, it can spontaneously ignite, which causes two 'firings' of the piston per one injection. This can cause a knocking noise, and is invariably bad for the engine.
Fuel stabiliser is a mixture of the higher octane hydrocarbons, which lower the overall likleyhood of pressure-induced combustion.
By adding fuel stabiliser, you can increase the octane of the fuel you are using, thus reducing the likelyhood of spontaneous (and unrequired) combustion.
Some fuel stabilisers also contain oil to lubricate the parts, if the engine is not sophisticated enough to keep itself oiled (eg your car's engine does this).
So by buying this 'stabiliser' you are increasing the lifetime of your equipment, not the efficiency of your fuel.