Factor validity is the degree to which the covariance of measured items matches the real covariance or behaviors in real life. It is a type of validity which is the degree to which a test is measuring what it is intended to.
For example, a test that asks a student questions about French movies is not a valid measure of the student's mathematical abilities. This would be an invalid measurement. Factor validity is related to context validity which is how well do the questionnaire items represent the construct being researched. Factor analysis is used to test the factor validity of a measure or questionnaire. Correlations between responses are clustered together by groupings of items in the measurement.