As noted by K Dog it is the not until the Electoral college actually sits and votes that the real election takes place. Technically, what we are doing today is electing the Electors.
Since the 60s, way to many historians have place an elitist connotation on the Electoral college but in 1792, it served several practical purposes.
-) First and foremost, it prevented vote fraud. It was easier to confirm the both the identities and votes a few dozen individuals all collected in one spot. Travel times dictated that only a handful of individuals from each state could be involved.
-) You have to remember that the word "State" has shifted meaning when applied to the U.S. acquiring a since of province or department but in 1792 it meant a Sovereign polity. If America was being named today, it might be called the United Nations of America as the two words have begun to overlap.
Many of the state seals displayed in courtrooms still have the state name proceeded with "sovereign". In the legal form for extradition between states, takes the form of "the sovereign state of New York request extradition of person 'X' from the sovereign state of Texas."
Therefore, the electors officially represent a sovereign polity with a federation. Just as with Senators originally, the Electors represented the State governments and the procedure for electing them varied. Universal white male suffrage only became universal in the 1850s and before then Electors were chosen by the State legislatures. South Carolina was the last to do so in 1860.
-) Basing the number of electors on the number of Federal Representatives plus two Senators for each state prevents the dreaded one-man-one-vote which despite the just sound of it, only works in small, homogenous populations. America has always been to physically diverse with large variations in population density.
Only members of the House of Representatives are elected by one-man-one-vote.
Alaska and Vermont both have populations of only mid-sized cities. Combined they have fewer than 1 million voters. Without the the automatic two Senators and thus two electors, the people of neither state would have any say in the Federal government. In 1792, this would have prevented the ratification of the Constitution. In times since, its allowed people whom we need to work way out in the sticks e.g. farmers, miners, settlers etc to still have a practical say in what goes on in Washington.
This was vitally important early on because the greatest threat to young United States was that European powers would manipulate states into leaving the Union and pick the country apart. That was the warning in Washingtons, parting address with it's famous line about "avoiding foreign entanglements." With extra influence at the Federal level, the smaller states could grow frustrated and believe, perhaps correctly, they would be better off on their own or allied to outside power.
-) The winner-takes-all-electors in a state system is also a means by which smaller states gain disproportionate representation and it also helps create a mandate for the President by giving the winner a big majority in the electoral college.
E.g. In 1860 Lincoln received 180 electoral votes, not only a majority but larger than all the other three candidates combined. But he only carried 39% of the popular vote with the other three gathering 18.1%, 12.6%, and 29.5%. He did not gain a majority of the popular vote but he won broadly enough that he had a decisive mandate in the electoral college.
(It was likely Lincoln acquiring the mandate without getting a single vote from a slave state, that triggered session. The Southern Slavearchs realized that from that point on, the South could be ignored by Presidential candidates and still win. Because of the regional block voting created by the contention of slavery, the South would never have real weight in the Federal government again.)
-) In principle, the Electoral college also serves as safeguard against someone manifestly unfit from becoming President. This is the origins of the concept of the faithless elector.
But since the Constitution makes a the specific point that the Electors are not bound, they're not being any less faithless, in the votes they cast than the standard representative who claim he will vote one way but in office fails to do so.
In 1792, the greatest concern was that some European aristocrat of some American with delusions of the nobility would try and slip through. Even outright imposters could not be ruled out in a nation so large and diverse. Presidential candidates didn't tour the country until after the Civil War and rise of the railroads. Local party members did all the campaigning. The type of background checks we take for granted now didn't exist, there wasn't any investigation close like finding out how much Sarah Palin paid for the drywall in her basement.
The original Electors were almost all senior members of the either the State government or the State's Federal delegation. Each State electoral delegation was part of an old-boys-network that could vouch for both the identity and minimal integrity of a candidate from their own state. In a system of direct election, someone known only from writings and and local speech makers (usually hired guns in any case) could get to the Presidency and, "surprise," you've got a king, or a candidate might have fallen ill, physically or mentally in the months since the election.
The Electors were originally elite political leaders collected from all over the country to give a final vetting of the candidates. Just in case.
The Founding generation, not just the political leaders but the entire electorate spent nearly a decade thrashing out the details of the Constitution. Every jot and tittle was scrutinized repeatedly. We have to put ourselves in their shoes and think about all the practical problems, things like travel times and identification, plus their understanding of history e.g. the English Civil War and the Glorious Revolution exerted a profound influence on their thinking, something we would hardly consider.
We probably could dispense with the actual electors today as technology has eliminated many of the problem they were created to solve, but we would still have retain the actual voting system. Otherwise, California, Texas, Florida and New York would run everything and no one else would have much say.
"A'int broke don't fix it" applies here.