First Past the Post elections, are those in which a population votes for candidates, and the one with the most votes wins.
For the parts of our government that are based on electing a proportionally representative staff to vote on legislation in a way that reflects the overall opinions of our country, such as congress, FPTP makes no sense, and is not used commonly outside the U.S and the U.K.
The following is a video explaining the problems of FPTP, which at first glance seems like a fine system of voting, but is in reality a gross misrepresentation of a populations political diversity.
The problem with First Past the Post:
http://www.youtube.com/watch?v=s7tWHJfhiyo
Next is a video on the more commonly used, Proportional Multiple Winner method:
http://www.youtube.com/watch?v=QT0I-sdoSX