What is the role of the prime minister?

A prime minister manages the politics of a country. With countries that have kings and queens (known as monarchs), they are very important because they are in charge of most of the politics (they are "head of the government"). In countries with a president, they might be in charge of most of the politics (as in the Republic of Ireland), or they may be in day-to day charge, but taking orders from the president as in France.