The short answer is that a when states hold elections for the President each state has a specific number of delegates, or as your friend said, points. These delegates are assigned by the population and some other metrics. Now, when the ballots are all counted the candidate with the plurality or most votes in that state gets all of those delegates assigned to it. For example if Texas has 25 delegates and a Candidate A wins the popular vote in Texas, Candidate A gets all 25 of those delegate votes when the electoral college convenes and technically elects the president.
However, this process has good and bad points. The best point about it is that the candidates generally have to visit every state. If we did not have the electoral college the only people that a presidential candidate would have to woo would be those in the major population centers of the country. Which would be the Northeast and the California in the west. This would disenfranchise a lot of voters in what we call "fly over country" which by and large has a completely different set of values than those who are in the urban population centers. The downside is that occassionally a presidential candidate does not have to receive the popular vote to get the presidency.
For example, take a look at this map http://www.usnews.com/usnews/news/election/map.htm. This is a map of the 2000 election for the presidency. You'll notice that the only states which went for Gore (blue) are those in the North Eastern part of the US and on our western coast. These are heavy population centers in our country and have a completely different set of values than those who are colored red. Gore won the popular vote, but Bush won the necessary amount of delegates.
Finally the United States is NOT a democracy. Our system of government is a representative republic. We elect our representatives through a democratic process and they are expected to represent our values when they go to Washington DC. Although it doesn't always turn out like that.

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These delegates are part of the electoral college
