I know that PCR is used to amplify DNA, but what do people mean when they mention 'PCR tests' for diagnosis of disease? And what does a positive/negative PCR test mean?
PCR tests would involve amplification of DNA before actual tests happen. PCR tests actually refer to tests that occur after PCR has been done. Most of the time when you look at PCR tests you see images like this
This is the result of gel electrophorosis, and not specifically PCR, as PCR only increases the content of DNA so that it is sufficient for gel e. to take place (if not you won't be able to visualize the bands, etc).
Diagnosis of genetic diseases are made available through similar processes (gel e., RFLP analysis). They are just categorically termed under PCR. They detect the presense of mutant or healthy alleles and subsequently whether the subject is tested positive or negative for the disease.