For hepatitis and HIV patients, one important use of PCR is determining the viral load, which is the amount of virus in the blood. Another use is finding the genotype of viruses, such as hepatitis B or hepatitis C.
Basically, PCR is a way to make many copies of specific parts of DNA (DNA is the complex molecule in our cells that carries our genetic code). This simple concept (amplification, in the language of PCR) is so important that the person who developed the process won a Nobel Prize for his work.
Before PCR, obtaining enough DNA for analysis was a time-consuming (days to weeks) and complicated process. Now, PCR can have the same result in hours. Having a relatively large amount of DNA to work with has made testing faster, cheaper and more accurate.
More detailed information about how PCR works is available in Theory Behind the Polymerase Chain Reaction.