@trinsec
To offer a bit more background: the US Constitution was written in the late 1700s. It could take weeks to communicate down the length of the country, which presented challenges we don't see today - organising a single nationwide vote of the general public was logistically impractical. So the framers laid out a multi-step process:
1. The general public casts their votes for Electors
2. Electors meet at the state capital to cast their votes for President
3. Each state sends its Electors' totals to Congress, who adds them up and determines the winner.

Conventional campaigning is about convincing people to vote a certain way at step 1, a "faithless Elector" who votes for someone other than his pledged candidate would do so at step 2, and the events of 6 January a couple years ago were an attempt to influence Congress's determination of the winner in step 3.

Each state has a number of Electors equal to the total number of its Representatives (proportional to population) and Senators (two per state regardless of size), so the framers might have expected the states to use the existing ridings with a couple at-large statewide races for the two Electors corresponding to the Senators, but this isn't codified and the details are left to the states. Two small states still do things this way, but most now award the whole slate of Electors to the candidate with the plurality at the state level.

There's some disagreement as to why most states are winner-take-all. I take the view that it's self-interest: for swing states, this increases the payoff for winning and means candidates spend more effort and money to win its citizens' approval; for stronghold states it means the dominant party assures itself of that many more Electors on its side. But there are others who see this as a purposeful choice by the framers to avoid mob rule, and see this as an invention of great wisdom (or even Divine inspiration) on their part.

Now that we have the ability to conduct a single nationwide election, it would make a certain amount of sense to implement this - but amending the Constitution is really hard. There's a sizable cohort of Americans who revere the framers as religious prophets and consider any suggestion of modifying their writings akin to sacrilege. On top of that, the current system gives a small but durable advantage to less-populous states, who would actively oppose any attempt to weaken their position.

So instead the workaround is that if a group of states which collectively comprise more than half the Electoral College all sign onto this compact, they'll each award their slates to whichever candidate wins the *national* rather than statewide vote, guaranteeing him a majority. As @Pat points out, the legality of the plan to have Congress approve the compact after the states agree is unclear, and circumventing the normal amendment process this way is controversial.

@peterdrake @sojournTime