It's fairly simple -- provided that you remember that the United States is a federal republic, not a democracy, and certainly not a Parliamentary democracy on the current European model. The distinction is by no means trivial.
Each State (there are 50 of them) is actually remarkably independent (something which sometimes drives people slightly crazy), and the Federal government is selected by the individual States. Each State has two senators, who sit in the Senate -- the upper chamber -- regardless of population; this was and is intended to keep some sort of regional balance among the States (and it works). Each State also has a certain number of Representatives. The number of Representatives is determined by the population of the State, with a minimum of 1 (such as places like Vermont or Montana or Alaska). They sit in the lower chamber, the House. The President is actually elected by Electors, and each State has a number of Electors which is the sum of the Senators and Representatives. The vote in each State determines which set of electors is picked; in most states it's winner take all, but in a few the electors are split proportionally with the popular vote.
The end result is a remarkably stable government, in which the interests of the people are pretty well balanced by the interests of the geographic regions.
Does that help?