Generally, engines burn oil due to a few reasons.
Bad valve seals: The valves are located in the engine block above the combustion chamber. Oil is pumped at 50 to 80 psi of pressure into the top of the head, lubricating the valve-train; the valves have seals to prevent oil flowing into the engine when the valve is open. If the seals fail, oil can flow down into the combustion chamber and is burned.
Worn valve guides: valve guides ensure valves move smoothly down their cylindrical chamber. When these guides wear over time, they do so unevenly, causing "slop" which allows oil to flow down the valve stem into the combustion chamber to be burned..
Pressurized crankcase due to clogged PCV or breather system: The car's engine is a giant pump, consequently it must breathe: air (and gasoline in, exhaust out). The PCV (Positive Crankcase Ventilation) system does just this, to enable the engine to excess pressures to exhale the exhaust gases. Carbon build-up is a by-product of burning hydrocarbon fuels in an engine and can accumulate in the PCV system, which starts to clog the breathing passages. This can cause pressures to rise in the oil pan and push oil into the fuel delivery system, causing it to be burned in the engine.
Blow-by from worn piston rings: The pistons in your car's engine have seals around them in the form of rings. These rings do two things: they seal the combustion chamber so no power from the firing cylinder is lost, and they apply vital lubrication to the cylinder walls. When the rings wear out, the pressure from combustion reverses down into the oil pan, pressurizing it and forcing oil into the valve covers, through the breather system, back into the fuel delivery system, and into the engine to be burned.