Suppose you are conducting a psychological or sociological survey of high school student attitudes towards teen drug use.  There are many things which might affect how accurately the responses actually reflect what the group being surveyed really thinks.  To what degree are people honest on surveys?  Are the questions worded in a neutral, non-judgmental way?  Was the survey given Friday at the end of the day when all the teens just want to go home?

Construct Validity is, in simple terms, an analysis of how a psychological or sociological assessment or measurement is put together.  From the eNotes reference search, this is an even better way to say it:

Are we actually measuring what we think we are measuring?

To have Construct Validity, the answer to that question must be yes.