Ceramic disc tap – The modern style tap (one where you only turn the lever a quarter for full flow) is known as a ceramic disc tap. If this is dripping from the spout then the whole central cartridge will need to be looked at and possibly replaced.
Stem or pillar tap – The more common tap is a stem or pillar tap (where the headgear is turned several times to control the flow of water). If a pillar tap has a dripping spout then the washer will need replacing. This is a problem