Adding tetraethyl lead to gasoline increases its octane rating. Octane rating is essentially a measure of how difficult it is to ignite the gas.

The reason it for wanting for gas to be harder to ignite is to eliminate a phenomenon known as knocking. When you compress the volatile gas/air mixture in an engine cylinder, especially when it's hot, it can ignite spontaneously. This is, in fact how diesel engines work -- the fuel is ignited by compression, not by a spark plug. Knocking occurs when the fuel in a gasoline engine is ignited by compression before the spark plug fires. (The knocking sound is actually the sound of the fuel igniting at the wrong time.) Higher octane gas, being harder to ignite, is less likely to cause knocking.

Why is knocking bad? Well, besides the annoying sound, it causes a loss of power because the energy generated by that bit of gas is largely wasted if the piston isn't at the top of its stroke when it ignites.

All that being said, there are better (i.e. not deadly poisonous) ways to increase octane ratings. One that was in relatively widespread use before GM and DuPont introduced leaded gasoline, is ethanol.