The business of Parliament takes place in two Houses: the House of Commons and the House of Lords. Their work is similar: making laws (legislation), checking the work of the government (scrutiny), and debating current issues.
The House of Commons is also responsible for granting money to the government through approving Bills that raise taxes. Generally, the decisions made in one House have to be approved by the other.
In this way the two-chamber system acts as a check and balance for both Houses.
The Commons is publicly elected. The party with the largest number of members in the Commons forms the government.
Members of the Commons (MPs) debate the big political issues of the day and proposals for new laws. It is one of the key places where government ministers, like the Prime Minister and the Chancellor, and the principal figures of the main political parties, work.
The Commons alone is responsible for making decisions on financial Bills, such as proposed new taxes. The Lords can consider these Bills but cannot block or amend them.
The House of Lords is the second chamber of the UK Parliament. It is independent from, and complements the work of, the elected House of Commons. The Lords shares the task of making and shaping laws and checking and challenging the work of the government.
I was unaware that British rule so closely parallels our system in the States. We have three branches of government each with checks and balances each branch has its own function. When I find it I'll post a link to a kids cartoon called school house rock that covers the subject.