A machine which separates compounds by the basis of their respective polarities by pumping solvent at high pressure through a column of packed silica.
A simple HPLC consists of a pump for solvent, a solid-phase extraction column, and some sort of detector (UV absorbtion, Visible absorption etc...) With multiple pumps, a mixing chamber and a computer to control it, a solvent gradient can be employed, that is, two solvents can be mixed so that the carrier solvent becomes more (or less) polar with time.
The column is a metal jacket packed with silica, but more complicated substrates can be used for analysis of specific species.
For the detection methods, the compounds in question must either absorb UV light, or absorb visible light. Depending on the flow cell design, fluorescence measurements are also possible, though most HPLC's are not equipped for this.
With the advent of API-ES (electrospray mass spectrometry) it is possible to have a LC-MS hyphenated system. (or LC-MS-MS if your lab has more money than God...)