What Is an Electoral College, and Why Do We Have One?
The Electoral College is how the US chooses its president. It reflects our "partly national, partly federal form" (Federalist 39) of government.
The Electoral College is composed of Electors delegated from each of the 50 states and 3 from DC. The number of Electors each state sends is the sum of the number of Senators and Representatives it sends to Congress. Thus, South Dakota has 3 because the entire State is one congressional district, while California with 53 congressional districts has 55. Each state legislature is responsible for choosing its Electors. All states except Maine and Nebraska (and possibly Colorado, after Tuesday) are "winner take all": whoever wins the popular vote in the state gets all the State’s electors. This way, the State retains the maximum possible impact on the outcome of the vote. Electors however are not bound to vote for the candidate who wins in their state (or their district, in the case of Nebraska and Maine); usually when an Elector "defects", it is merely as an inconsequential protest vote. State parties determine the identity of the Electors; they are usually people with long track records of party service.
A majority (270) of the electors in the College is needed to choose a President. If no candidate wins a majority, the House of Representatives decides, each state delegation having one vote. A majority of the States are needed to elect a President.
Why do we have an Electoral College? Why not have direct majority elections instead?
Like many provisions in the Constitution, the College was the result of compromise between large states and small states. It may be fairly argued that states are less important today, given the nature of interstate commerce. Two sorts of arguments can be made here: practical and theoretical.
The Practical Argument:
Since the Electoral College is established in the Constitution (see Twelfth Amendment), it will take a constitutional amendment to change it. Amendments to the Constitution take ratification of three quarters (ie, 38) of the states. Since the 21 smallest states combined have a population less than California's, it is unlikely that they will cede their disproportional electoral influence to the more populous states. For example, Wyoming has 3 Electors, or 1 for 167,000 residents. California has 55 electors, or 1 for every 727,000 residents. Is it possible that Wyoming will ever give up its votes when it can only lose and not gain from the arrangement?
The Theoretical Argument:
If we take national popular majorities to be a better method of determining leadership than state by state representation, then we might as well do away with the Senate as well. (This is actually impossible: no amendment to the Constitution can deny a State its equal representation in the Senate without its consent—see Article V.) After all, it is disproportionate representation in the Senate that gives small states their influence in the Electoral College.
Undoing the College would certainly weaken federalism, viewed by many as an essential check on powerful central government. States would cease to matter electorally, so large geographic areas of the country would tend to be permanently ignored by presidential candidates.
For better or for worse, it is the Constitution which establishes the form of government which Americans have today. As parties to the Constitution, the states through their legislatures (or popular conventions) have to approve changes to it. Whether or not we consider ourselves Marylanders or Minnesotans, when we vote for President, that is how we are counted.