The primary advantage of a parliamentary system is that it makes the government accountable to the citizens for the decisions it makes by creating a group to monitor its performance. It also provides an out through a no-confidence clause that could scrap a government doing a poor job and call for re-elections.
A parliamentary government is similar to the checks and balances systems of the U.S. government, except the house of parliament is technically outside the realm of government. The one exception to this is the role of the prime minister, who is simultaneously a member of government and a member of parliament.
Parliamentary government also basically grants control of the government to the party that wins the most votes in an election and provides it with the support necessary to implement the winning platform selected by the people. Because of parliamentary structure, it is possible for parliamentary governments to fulfill promises made to citizens during elections without the stalemates that are sometimes encountered in the American system when the parties are unable to come to an agreement. This is because, in the American system, all parties have the power to act in accordance with their own agendas when it comes to passing bills into law.