Factor analysis is a numerical technique used to explain variability among observed, connected variables in terms of a potentially lower number of unseen variables called factors.
For example, it is possible that variation in six observed variables mainly reflects the variations in two overlooked variables. Factor analysis searches for such joint variations in response to ignored latent variables.
The observed variables are modelled as linear combinations of the potential factors, plus “error” terms. Factor analysis aims to find autonomous latent variables.
The theory behind factor analytic methods is that the information increase about the interdependencies between observed variables can be used later to cut the set of variables in a dataset.
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(Source: https://www.quora.com/What-is-the-use-of-a-factor-analysis)
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