It may seem crude, but this method actually works.
Usually when you're stuck behind a car that's spewing bluish white smoke from its tailpipe, the temptation to roll down the window and tell its driver that oil is leaking into the engine is a strong one (unless you don't like to use your gearhead powers for good that is). Technically all engines burn oil, but Formula 1 engineers develop their cars to burn more than the average car. Why would such a wasteful tactic be utilized on vehicles that need their power plants in top competition shape?
To answer that, it's best to turn to a real engineer who seems to have spent quite a bit of time exploring F1 technology as of late. The main reason Formula 1 cars benefit from burning oil is that they get a nice power boost to help when accelerating out of the corners.
When oil sneaks into an engine either through the Positive Crankcase Ventilation system or by passing the piston rings by clinging to the the cylinder walls, it combusts along with the gasoline and the resulting explosion helps the piston make more power than if only gasoline was burnt in the combustion chamber. Given how tightly regulated fuel is in F1 racing, teams can take advantage of the fact that oil is regulated more loosely to make extra power by mixing combustable additives into the oil and letting more of it seep into the combustion chamber. The only catch? The fact that Formula 1 regulates how much oil each engine can burn. Still, this is a pretty clever way to use any discrepancies in the rules to your advantage.