The "lifter" is a cylindrical device that rides on the "camshaft". Its job is to transfer the rotary motion of the camshaft into linear motion, based on the "lobes" of the camshaft. This linear motion it transmitted through a "pushrod" to a "rocker arm" which reverses the linear motion and transmits it to the end of a "valve". The "valve" is located in the "head" of the engine, more specifically the "combustion chamber". The "valves" are used to introduce an air/fuel mixture into the "cylinder" as well as expell the exhaust gases after combustion.
Typically, on late model vehicles and many other non-performance vehicles, the "lifter" is a hydraulic unit that "pumps up" with oil pressure. When it "pumps up" it closes the tolerances, or gaps, between the "push rod", the "rocker arm" and the "valve". If the hydraulic nature of the "lifter" is comprimised (via mechanical breakage, or some other failure), the lifter will not "pump up". This failure will result in the tolerances not being reduced and the rocker arm "tapping" or "slapping" the end of the valve by the "rocker arm". That "tapping" or "slapping" of the valve results in a "ticking" noise in the engine...and hence, we have the "noisy lifter".