Nothing, for awhile. But eventually the valve lash on your engine will loosen up or close up. On valves where it loosens up, it will make noise and accelerate rocker arm and valve tip wear. On valves where the lash closes up, it will cause the valves to leak and burn.
Periodic valve lash adjustments are required because most of these engines have mechanical lifters or cam followers. These were used to cut costs (and boost performance, some might argue). Hydraulic lifters are more complicated and expensive, but run much quieter and eliminate the need for period valve lash adjustments. Hydraulic lifters or followers are now used on almost all engines. But if you're driving an engine that doesn't have them, you'll have to live with periodic valve lash adjustments or suffer the consequences.
The valves are adjusted on pushrod engines by changing the height of the rocker arm or turning an adjustment screw on the end of the rocker arm. The clearance between the tip of the rocker arm and valve stem is adjusted to a specified clearance which is measured with a feeler gauge. The spec may require the lash to be set with the engine hot or cold. It makes a difference so always refer to a shop manual for the exact clearances and adjustment procedure.
It's also important to note that the specified valve lash for exhaust valves is often greater than that for intake valves. This is necessary because exhaust valves run hotter than intake valves and grow longer due to thermal expansion when the engine heats up.
Each valve must be adjusted with the piston at top dead center so both valves are closed and the lifters are resting on the lowest portion of the camshaft. The best approach is to start with cylinder number one, then proceed in the engine's firing order.