The Althing, the national parliament of Iceland, was founded earlier (930 AD), so it is the oldest legislature in the world still existing. However, the Althing did not function as a legislature for four centuries, and its role as a primary legislature is modern.
Other parliaments have copied the UK and work similarly. They have three levels - a lower house which makes the law, an upper house which reviews the law (Decides if they like it or not, and suggest changes to it), and a head of state who is mostly for show and who starts and ends each year of parliament. The Prime Minister is almost always the person whose party has the most seats, but if the lower house does not think he is doing a good job they can call a vote of no confidence and ask him to leave his job as Prime Minister or have an election.