Valve lash is the mechanical clearance between the camshaft lobe and the valve stem or rocker arm (sometimes called a transfer rocker) when the valve is fully closed. It's usually checked with a feeler gauge. On non-self adjusting mechanical valve lifter mechanisms, the value is normally non-zero.

See: Internal combustion engine valve actuation methods for more details on camshafts and valves

Different expansion characteristics cause the cold clearance to be different than the running/warm clearance. Margin is built in to make sure their is always some clearance, especially on exhaust valves. An exhaust valve that fails to close completely doesn't transfer enough heat back into the head and can "burn".

Why does valve lash need adjusting?
Too much valve lash can accelerate wear on the rocker arms, cam followers, camshaft lobes, valve stem tips and valve seats. How much it does depends on the engine, and, how far out of spec the lash is. Too much lash also tends to make more noise, so you're more likely to know it needs adjusting.

Too little lash is more dangerous both because it leads to more serious problems and because it doesn't make any noise. If the lash is too small, the valves may not seat properly when the engine warms up; causing a loss in compression and valve damage.

Valve lash has a tendency to expand instead of contract as the components of the valve train wear in and age, therefore valves which tighten up are not a big risk unless improperly adjusted.

How often should I check my valve lash?
I've been told that generally to check valve lash every 20 to 30 thousand miles. Some suggest every other oil change, some suggest every 60 thousand miles. YMMV.

Note: most modern vehicles do not have valve lash requirements as they are self adjusting.

Sources: Information obtainable and provided by most automobile forums.