Definition: Factor analysis is a statistical technique used for replacing a large number of variables with a smaller number of “factors” that reflect what sets of variables have in common with one another. It is commonly used in an exploratory way to identify what underlies a set of otherwise loosely related variables.
In many studies, the construct of "leadership" has been observed to be composed of "task skills" and "people skills." Let's say that you are developing a new questionnaire about leadership and you create 20 items. You think 10 will reflect "task" elements and 10 "people" elements. When you analyze your data, you do a factor analysis to see if there are really two factors, and if those factors represent the dimensions of task and people skills. If they do, you will be able to create two separate scales, by summing the items on each dimension.