The purpose of the electoral college was put in place to create a balance between high-population states and low-population states during presidential elections. That's the simple answer, if you want a more in depth answer as to how it functions I'll have to refer you elsewhere.

Likewise each state of the union has two senators to serve in the upper house of our legislature. (The lower house has a number of representatives that correspond to the state's population.)

It was a concern of the founding fathers of the nation that urbanized, heavily populated states would have an unreasonable degree of power over rural, less populated states. See, in theory the USA is simply a union of quasi-independent states that are all considered equal to one another. California and Wyoming are equal peers, just as New York and Mississippi are equal on the national stage. Despite stark differences in population and economic activity, they all stand on equal footing when it comes to governing the union as a whole.

It is not a perfect system, but it's the best that could be agreed upon when the Constitution was written. (And for better or for worse, works fairly well most of the time.)