Parliamentary systems often work where the head of government is the leader of the political party with the most members in the parliament.
The separation of powers between the executive and law making branches is not as obvious as it is in a presidential system. There are different ways of balancing power between the three branches which govern the country (the executive (or ministers), the law makers and the judges).
Parliamentary systems usually have a head of government and a head of state. They change after their terms are over. The head of government is the prime minister, who has the real power. The head of state may be an elected president or, in the case of a constitutional monarchy, hereditary.
Examples of a few countries which practice parliamentary systems are India, Italy, Japan, and Latvia to name a few. Parliament is different in every country.