From Academic Kids
Indirect election is a process in which voters in an election do not actually choose between candidates for an office but rather elect persons who will then make the choice. This process is used in many union elections and sometimes in professional, civic, and fraternal organizations, but it is best exemplified in the election for President of the United States, in which voters elect not a Presidential candidate but rather a slate of candidates for the Electoral College, which then elects the President. A similar process has been used in the past in emerging democracies, i.e., South Korea and the Republic of the Philippines, but it was soon dismantled in favor of direct election. Only in the United States has a process of indirect election persisted for over two centuries.
Some argue that a parliamentary system is in fact an example of indirect election. While members of the parliamentary body are elected directly, it is their votes, usually cast for their party leader, which determine who becomes Prime Minister. However, a Prime Minister is more a representative of the parliament, a 'primus enter pares' (first among equals), who has just one vote, just like any other member of parliament, and therefore doesn't quite have the amount of power that presidents tend to have. Such a system tends to make all elections more about national issues than is generally the case in the U.S., where it is very commonplace for some districts routinely to vote, often by a large majority, for a Presidential candidate from one party and a member of Congress from the other. Then again, a parliamentary system usually also has separate elections for lower governments (such as city or province). So the same system may be used at different independent levels, possibly even with different parties.