The purpose of a valve lifter is to transmit the thrust of the camshaft to the push rod (or valve rod) and to withstand the lateral force exerted by the rotation of the camshaft. The tappet has an adjusting screw at its top for adjusting the valve clearance.
Hydraulic tappet, also called valve lifter or hydraulic lash adjuster, is a device for maintaining zero valve clearance in an internal combustion engine. It helps get rid of the need for combustion engine to have mechanical clearance in the engine's valve train, to keep the valve from being held open and thus destroyed as the valve train goes through its process of thermal expansion. In effect, valve lifter keeps the valve healthy and protects from an engine's normal thermal expansion process.
Hydraulic lifter helps to ensure less engine noise and longer reliability, due to less wear and tear. A faulty hydraulic lifter will usually result in the rocker arm, valve tip and push rod also going bad if left unattended. If an engine with hydraulic lifters is noisy, then either the internal spring has lost some tension or the check ball is not sealing or allowing the oil to fill the cavity. For all practical purposes, the tappet needs to be replaced.