A head gasket is a gasket that sits between the engine block and cylinder head(s) in an engine. Its purpose is to seal the cylinders to ensure maximum compression and avoid leakage of coolant or engine oil into the cylinders; as such, it is the most critical sealing application in any engine.
If the gasket fails, a variety of problems can occur, from compression loss (leading to power reduction, or a rough engine), to exhaust gases being forced into the cooling system, leading to the engine overheating and increased engine wear due to the motor oil being mixed with antifreeze. Coolant can leak into the cylinders, causing the exhaust to issue steam and the catalytic converter to be damaged. If a very large amount of coolant does this, hydrolock can occur, causing extensive engine damage.