Face validity is a cumbersome statement about the meaning of a variable.
When you collect data, you usually use a test or a questionnaire. The test or questionnaire - or more generally: instrument - must be tested for validity and reliability. However, sometimes the researcher does not have time to test the instrument and so really nothing can be said about its validity. The best he could say: Well, it doesn't seem so bad to me; I think it's okay. This is face validity.
In my opinion, this is a very bad view of validity. The test or questionnaire may look good to the researcher, but is it really a good tool? Does it provide useful information? There is no evidence whatsoever. If an instrument only has face validity, this does not mean that the research is useless. It simply means that it is not in accordance with the foundations of science in which use is made of validated measuring instruments.
In my opinion, it is best to remove face validity from the list of scientific terms. It just means: "I don't know, but it seems fine to me."