Factor Analysis has to do with determining if a group of scores can be broken down into subcategories or factors. Scores tend to group together and this trend is determined through factor analysis.
Example: If 100 students take a test and 50 of them do well on the first half and the other 50 do as well on the second half, we could argue that this test actually measures 2 different factors.
This is often useful in determining variables that are unknown. Some common variables that were determined using this method, include: