A hydraulic lifter takes the place of the older valve tappet where a small space was left between the valve and the camshaft (or rocker arm). The tappets were noisy and required adjustment to maintain the correct clearance due to temperature and wear.
A hydraulic lifter works by filling the space between the valve and lifter with pressurized oil. This provides zero valve clearance which is quiter and performs like a solid lifter because the oil is incompressible.
Drawbacks are that the oil can drain down while the engine is off and then the lifters rattle for a few seconds at startup until the oil fills the space and the pressure comes up. This normally isn't an issue but a permanently rattling lifter typically indicates that the oil passage is blocked or there is some other mechcanical problem with the lifter and should be investigated.
Wayne over at Pelican Parts has a very nice write up on what it takes to get to those noisy lifters and Fig. 13 shows a very nice picture of the lifters:
http://www.pelicanparts.com/techarticles/Boxster_Tech/16-ENGINE-Camshaft_Swap_and_Chain_Tensioner/16-ENGINE-Camshaft_Swap_and_Chain_Tensioner.htm