A parliamentary system that is based on the Westminster model (though several other models use this division as well) is usually comprised of two main divisions: the government and the opposition. The United Kingdom and the Commonwealth refer to the Opposition as "His/Her Majesty's Loyal Opposition."
This dates back to the foremost days of the Westminster-based system. The monarch had the option of inviting whichever party won the most seats in a general election to form a government. If the monarch made this offer and the leader of the victorious party accepted, the members of parliament from other parties became the Opposition. The collective name for the Opposition refers to the fact that the other parties, despite any differences they may have with each other, will hold the government accountable for any decisions that may be questionable. The Opposition is loyal to the institution of parliament as a whole and to the Crown. Its main job is to question the government with the interests of all citizens in mind.
The party with the second most seats is usually known as the "Official Opposition." Its leader is known as the Leader of the Opposition (though sometimes the 'Her Majesty's Loyal' part is also included). In the Westminster-based House of Commons model, the Leader of the Official Opposition sits directly across the aisle from the Prime Minister in the House, as it is his or her main parliamentary function to debate the Prime Minister. With this title comes, in several countries, an official residence and a fair amount of media attention. The Opposition Leader is usually asked for comments whenever the Prime Minister makes any kind of a public statement.
It is often common for all other parties (space permitting) to also be seated on the Opposition side of the House. In the event of a minority government, the combined opposition outnumbers the government and therefore some opposition parties must sit on the side of the house traditionally reserved for the government. This is currently the case in Canada, where the minority Conservatives sit next to the opposition Bloc Québécois. The Liberals, who are currently the Official Opposition, share the opposition benches with the also-opposition NDP and some independents.
Just as the Leader of the Official Opposition has an assigned seat in the House of Commons, the leader of the opposition party with the second most seats also has a traditionally-assigned seat. This, as Txikwa points out, is true in the Canadian system but not in the British system, as the House of Lords has traditional leaders.
The Government/Opposition system also applies in the upper Houses of parliament. Members of these houses are not usually elected, however, and it is possible that the Official Opposition in such a House is different from the party that forms it in the House of Commons.
The Leader of the Official Opposition, in conjunction with his or her party, often appoints a "shadow cabinet" -- that is, a group of MPs that are assigned to "shadow" a government ministry. These members are seated directly across from the cabinet ministers they criticize, and attempt to hold them accountable for their actions during parliamentary proceedings.
While all opposition parties are given the opportunity to question the government during Question Period or Question Time, the Official Opposition is permitted to ask more questions more often. The Leader of the Opposition gets to question the government first, and the Official Opposition's questions usually come before those of any other parties. This party also receives more funding than the other party, but (obviously) not as much money as the government. (spiregrain notes that parties don't receive such funding in the U.K., though they do in Canada -- where all parties receive just over one dollar per vote received in the most recent election used to receive one dollar per vote received in the most recent election. Also, Canadian opposition parties that have attained official party status receive funding for office space and research; this depends on their rank in the House.)
Loyal Opposition - Wikipedia http://en.wikipedia.org/wiki/Loyal_opposition 18 January 2005
I also remember paying rapt attention to this stuff when it came up in grade four social studies.