Factor analysis is a method of analyzing a set of correlations to discover which variables in the set are correlated with each other but are largely independent of the other variables. Thus, factors represent the underlying processes that hold together each subset of correlations.
Factor analysis can account for a large number of variables with a smaller number of more basic dimensions. These more basic dimensions can be called traits, that is, factors that represent a cluster of closely related variables. Ex: we may find high positive inter-correlations among test scores in algebra, geometry, trigonometry, and calculus. We have now identified a cluster of scores that we might call Factor M, representing mathematical ability.