See other issues.
The United State of America was originally set up as a coalition of individual States and not as a simple government of people as many people now imagine it to be. The people at the time of the nation's founding were very concerned about the possibility of a federal government growing into a tyranny and usurping their right to be governed as they saw fit.
Separation of powers served to weaken and divide the federal government into competing interests that would be agile enough to serve their purpose, but dependent on the states for their power, making it more difficult for them to usurp the states' authority. The federal government depends on the states via its bicameral legislature, comprised of the house (congress) and the senate, and also through the electors who choose the President. The original intent of this system has not been completely preserved, but the electors are still an important part of the system that preserves states' rights.
The senate is one of those areas where the system has not been preserved, and there are many that argue that such failed preservation is a key part of the reason for the tyrannical government overreach we see today. Each state gets two senators. Therefore, by passing legislation through the senate, the legislation goes through a process by which states' interests are balanced equally. Each state gets two votes.
Regarding senators, the Constitution says "The Senate of the United States shall be composed of two Senators from each State, chosen by the Legislature thereof for six Years". Hence the legislature of each state picked their senators. They were a true representative of states' interests and served to directly serve the interests that each state had in preserving their rights and authority. However, in 1913, the 17th amendment to the Constitution was passed, which stated, in part, "The Senate of the United States shall be composed of two senators from each State, elected by the people thereof, for six years". This effectively made the senators directly dependent on the people for their authority, and while this might seem like a good thing (the amendment did pass after all), it also meant that states had nobody in the legislature serving to defend states' rights against federal overreach, which was, really, the entire point of the Senate to begin with. It is probably not an unconnected coincidence that we see significant deterioration of states' rights dating from about this time. (Expand on this. What were the concerns at the time that the 17th amendment was authored and passed.)
Congress, however, is the natural defender of the people. Congressmen, (ie. representatives) were and are elected by the people, and their numbers in congress, from each state, are proportional to the population of each state, with the caveat that each state gets at least 1. (Which helps to ensure that people from less populous states can be represented.)
The electoral college is something of an amalgamation of both of these ideas. Each state gets an elector for every senator and representative of the state. Hence there are two for each state, plus at least one or more other electors as determined by population. Less populous states, then, get even more of a relative boost to their representation among the electors, than more populous states. Effectively, giving rural states a relative boost in the strength of their voice. This effectively makes it so that candidates who win with popularity in more rural states (generally, Republicans) will be much more likely to see a discrepancy between the popular vote and the electoral vote. The effect of eliminating the electoral college, would, most directly, lead to a diminishing of the voice of rural America, centralizing power even more solidly in urban centers. Somewhat less directly, this would reduce the ability of rural states to defend their rights and lead to more rapid federal overreach. As has happened in many tyrannical governments, the rural farmer is oft overlooked and oppressed and suffers greatly. Modern Venezuela and the old Soviet Union are excellent examples of this. Unless the tyrant recognizes how vital these farmers are, and grants them special privileges, the result is almost certainly devastation of the country's agriculture, and hence, famine.
- PragerU, "Popular Vote vs. Electoral College", Facebook, 18 May 2015