The Electoral College was established in Article II, Section I, of the United States Constitution, and was later modified by the Twelfth and Twenty-third amendments, which clarified the process.
When U.S. citizens vote for president and vice President every election cycle, ballots show the names of the presidential and vice presidential candidates, although they are actually electing a slate of "electors" that represent them in each state. The electors from every state combine to form the Electoral College.
Each state is allocated a number of electors equal to the number of its U.S. Senators (always two) plus the number of its U.S. House representatives (which may change each decade according to the size of each state's population as determined in the census).