The executive is the branch of government that is responsible for the day-to-day management of the state. (Executive is short for executive branch or executive power.)
Under the doctrine of the separation of powers, the executive is not supposed to make laws (role of the legislature), nor to interpret them (role of the judiciary). The executive is supposed to put the laws into action.
The executive is led by the head of government. The head of government is assisted by a number of ministers, who usually have responsibilities for particular areas (e.g. health, education, foreign affairs), and by many government employees or civil servants.
In a presidential system, this person (the President) may also be the head of State, but in a parliamentary system, he or she is usually the leader of the largest party in the legislature and is most commonly termed the Prime Minister (Taoiseach in the Republic of Ireland, (Federal) Chancellor in Germany and Austria). In France, executive power is shared between the President and the Prime Minister and this system has been reproduced in a number of former French colonies. Switzerland and Bosnia and Herzegovina have similar systems.