What is the composition of Parliament and what are its main functions?

Parliament is made up of the House of Commons, the House of Lords and the Queen (the Queen-in-Parliament). Parliament is the British legislature: its role is to pass laws, and it has what is known as parliamentary sovereignty, which means whatever it passes becomes law, with no one (usually not even courts) being able to override it.

The House of Commons is the elected chamber of Parliament. It is made up of 650 MPs, each of which represents his or her constituency (i.e. the part of the country which has elected her and which she represents). The House of Commons has the role of choosing the Prime Minister, who is proposed by the Queen and has to "command" the Commons' "confidence". MPs are members of different parliamentary parties (e.g. Labour, the Conservatives, the SNP...), which advocate the same political goals and lobby together.

After a Bill is passed by the Commons, it moves on to the House of Lords, the unelected body of the House of Commons, made up of "Lords Temporal" and "Lords Spiritual". The Lords is also made up of parliamentary parties: however, it has a substantial amount of "crossbenchers", people who don't belong to any political party. In most cases (those not included in the 1911 and 1949 Parliament Acts), the House of Lords has to pass Bills before they are presented to the Queen for royal assent.

Once a Bill is presented to her, the Queen, through a constitutional convention, has to grant it royal assent. It is only then that the Bill becomes an Act of Parliament, and thus law.