Prime Minister is the term describing the chief member of the Cabinet in a Parliamentary system of Government. It can also be used to denote an official in a Presidential system or Semi-presidential system whose duty is to execute the directives of the President and manage the civil service.
In several parliamentary systems, notably the British, the Prime Minister is the head of the government, as opposed to the Head of State. Prime Ministers can be found in both constitutional monarchies (as is the case in United Kingdom and Australia), and in republics, where the head of state is an official elected (as is the case with the president of India and Ireland) either by direct election or indirectly by parliament. This contrasts with a Presidential system, where the President (or equivalent) is both the head of government and state.
Many presidential or semi-presidential systems such as France or Taiwan also have prime ministers. In these cases, the prime minister is an official generally appointed by the legislature who is responsible for carrying out the directives of the President and managing the civil service. In these systems, it is possible for the president and the prime minister to be from different political parties, a situation which is known as cohabitation.