In the UK we have a 'First Past the Post' form of democracy. This means whoever wins the most votes in a constituency wins that seat in parliament. Whichever party wins the most seats in parliament forms the government and the leader of that party becomes prime minister and it is seen that the country has given the endorsement for that party to fulfill their manifesto (the party manifesto is what they said they would do if they got into power).
When America set up their political system they thought this was undemocratic as it means that sometimes a party can be given authority to put their manifesto into place because they have a majority of seats even though they actually have less than the majority of votes (eg only 40% of the vote). Also it can give power to the least elected minority party (ie the smallest number of seats in parliament)who ally with the government against the opposition and pass all their manifesto in parliament.
The other thing is in the UK if you have, say, only 50% of the country turn out to vote coz of voter apathy, the real result is that the country is being governed by someone and their party with only relly 20% of the populations say so.
Also, say like dear Maggie Thatcher, someone can rule and rule the country with their party for as long as they are kept in even with such a low vote of the population.
The Americans thought all this was undemocratic.
So in America you have the separation of powers and checks and balances so this cant happen. There is the president, then congress, then senate. The leader, the president, is not necessarily going to the same as the congress and senate as they are all elected separately not like in UK where the party with the most seats puts their leader in power (like now we have an unelected head of country when Tony resigned and Gordon Brown in place).
Also the president can only serve two terms and is elected every four years. In the Uk they have to go to an election after I think it is 5 or 7 years but they can go whenever they like in that time, giving the party in power an advantage to pick and choose when they are popular with the country to get in again for another term of office.
So how we in UK have a First Past the Post system the Americans decided to have the electoral college. That way even if voter turn out is low etc the same 'votes' are always cast. Each state has so many electoral college seats depending on their population and makes it fair for all states to be important. Eg Clifornia has a lot but Wyoming has I think 3, it is good to win California but you have to get half of all the electoral college votes so need the small votes too.
So in for example clifornia if their were 10,000 people whovever got over half would win those electoral college votes, and whover gets half of all electoral college votes wins the presidency. After the winner is chosen it takes a few weeks for them if you watch to become the proper president as this is when the electoral college votes take place. The electoral college reflects business, trade unions etc to provide a further check and balance and ensure it is totally democratic so if for some reason they thought it was a fix they do actually have the power to use their votes a different way (but this doesnt happen).
The third option to these two democracies is proportional representation which means one vote per person, and then say the lib dems got 33% of actual votes they would get 33% of votes in parliament. This is completely fair but in reality can mean their is no one majority party and nothing gets done, and the 'real' power again goes to the smallest of all parties who hold the balance of power.
I hope this helps. It's waffly bollocks but I actually find it helpful to understand the world. Why people look to America as the ultimate democracy and when new democracies such as in Africa are being set up which political model they choose and that helps explain where all the tensions arise from when you see conflicts happening with them...
let me know if it helps or you want more info. Politics is so important to understand I applaud you for wanting to know more and apologise for all my spelling errors in advance