These are parameter files for rendering Jim Muth's Fractal of the Day images. The parameter files can be used with Iterated Dynamics to render the associated fractal image.
Most of the PAR files have already been rendered as high-resolution 1600x1200 images at the link above.
Les St. Clair grouped together all the Fractal of the Day par files and formulas and grouped them by volume, one volume per year. These are more convenient for browsing/loading the entire collection. These parameter and formula files are in the grouped directory.
If you have PAR files for dates not represented here (2003 through 2016 are believed to be complete), please open an issue and attach the missing PAR files (copy/paste may corrupt inline color table entries, so attachments are preferred). A ZIP archive can be attached to an issue as well, so you needn't attach individual PAR files.
If you're knowledgeable about git and github, then pull requests are also acceptable!