A set of PAR files is often posted accompanying a RAR file set. PAR files are parity recovery files that can be used to recover missing or corrupted segments of a RAR file set. PAR files usually have names such as movie.part01.p01, movie.part01.p02, etc.; you may also see movie.part01.par, but generally PAR files begin with .p01.
If all of the segments of a RAR file set are present and valid, you do not need any of the PAR files. However, if any RAR segment is missing or corrupted, it can be recovered by using a PAR file. It takes one PAR file to recover each missing or damaged RAR segment. So if a file is posted with 10 PAR sections, up to 10 damaged or missing RAR segments can be recovered. The only exception to this is the PAR segment with the .par extension. The .par file is optional and contains only information about what files are part of the set; it does not contain recovery information. Usually, .par files are not used; they are never needed. The actual recovery PAR files begin with .p01.

PAR files are independent of each other, so a missing or damaged PAR segment will not affect the recovery as long as there are enough good PAR files to replace missing and damaged RAR files.

SmartPAR is a free program that supports PAR files. You can download it here.

Why doesn't WinRAR support PAR files?

As of WinRAR 3.0 you can use .rev files to recover missing
volumes. Please read the chapter about "Recovery volumes" in the Knowledge Base.

We don't support .par files, because our .rev files supports a better
method to reconstruct missing files and to repair corrupted volumes
directly with WinRAR/RAR.