The UK uses a bicameral parliament with two houses - the House of Lords and the House of Commons. The former consists of appointees and the latter is the primary house of government. Members of Parliament serve in the House of Commons and are elected from regions within the United Kingdom (known as ridings or constituencies). Whichever party has a majority of votes in the House of Commons receives the right to form a government, and the head of that party becomes the Prime Minister, the head of government and de facto head of state. Because the elections of MPs uses a first past the post system, it is conceivable for a party to win an overwhelming majority of seats without winning a majority of the popular vote, especially whereas the UK has three primary parties in the House of Commons (the Conservatives, the Liberal Democrats, and Labour).
In the situation which appears most likely on Thursday, a hung parliament may occur. According to precedent, the party that recently formed a government (Labour) will be given the first chance to form a government. If Labour can survive confidence motions over the first few months, their government may survive for a longer period of time. They may form an informal or formal coalition with one or more parties to maintain governance. In an informal coalition, Labour will agree to give another party's platforms standing in return for that party's support on some issues. In a formal coalition, Labour will invite members of another party(s) to become Cabinet Ministers and have a closer-to-equal say in government.
If a confidence motion quickly defeats the Labour government, then the Conservatives may be given a chance to form government at the discretion of the Cabinet Secretary and Her Majesty the Queen. David Cameron, head of the Conservatives, has suggested he may also ask HRH Elizabeth II for permission to form her government if he wins a plurality of seats, but not a majority, and violate the convention I previously mentioned. Labour may forstall this by entering into a coalition with the Liberal Democrats, but noone really knows what Clegg will do (I think it's Nick Clegg who leads the LDP).
In other words, it's one of the more interesting UK elections since a fellow named Churchill ran.