From Wikipedia:
A hydraulic lifter, also known as a hydraulic tappet or a hydraulic lash adjuster, is a device for maintaining zero valve clearance in an internal combustion engine. The conventional means of adjusting valve actuation always requires a small clearance to be left between the valve and its rocker or cam follower to allow for thermal expansion and wear. The hydraulic lifter was designed to ensure that the valve train always operates with zero clearance, leading to quieter operation and eliminating the need for periodic adjustment of valve clearance.
The hydraulic lifter consists of a hollow expanding piston situated between the camshaft and valve. It is operated either by a rocker mechanism, or in the case of one or more overhead camshafts , directly by the camshaft. The lifter is filled with engine oil intermittently from an oil galley via a small drilling. When the engine valve is closed, the lifter is free to fill with oil. When the valve is opening and the lifter is being operated by the camshaft, the oil feed is blocked and the lifter acts just as a solid one would, oil being incompressible
There are a number of potential problems with hydraulic lifters. Frequently, the valvetrain will rattle loudly on startup due to oil draining from the lifters when the vehicle is parked. This is not considered significant provided the noise disappears within a couple of minutes, typically it usually only lasts a second or two. A rattle that does not go away can indicate a blocked oil feed or that one or more of the lifters has collapsed due to wear and is no longer opening its valve fully. The affected lifter should be replaced in the latter situation.
In certain circumstances, a lifter can "pump up" and create negative valve clearance so that its valve cannot close. Typically this occurs in the most upper rpm range of an engine, and limits the engine's performance. Lifter pump-up is serious, as there may be interference of the valve with the piston or, burnt valves may result. In all cases it is important to follow the manufacturer's recommendations for oil viscosity and quality.