Your system is similar to ours, except our vote is non transferrable. If your MP (is that what you call the person who stands for your constituency (local area)?) gets the most votes in your constituency, he/she gets a seat in the parliament. As soon as a party gets the majority (more than 50% of the seats in the parliament) they are the government, and their leader is the prime minister. If no party has a majority (45%, 45%, 10%) then a coalition will be formed between two parties to make a majority. The party who comes second forms Her Majesty's Opposition. All other MPs not in the government or the opposition sit around somewhere and still get to debate/vote on issues when they want.
That's it in a nutshell, like all things to do with British politics it's really much more complex than it looks.
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