The Advanced Scientific Data Format (ASDF) is used to store models for axes manipulation and rules that serve to exchange information with scientist of between stages of the calibration pipeline. This format is used by some reference files and also in some of the science calibrated products.
ASDF is a human-readable, hierarchical metadata structure, made up of basic dynamic data types such as strings, numbers, lists, and mappings intended as an interchange format for delivering products from instruments to scientists or between scientists.
For JWST, ASDF files are added to certain JWST calibration pipeline products or are part of the calibration pipeline reference data used by the software. In some cases, these provide with the distortion and spectral models needed to transform detector positions to a world coordinate frame along with the rules to combine them. Another use for these files is to provide with the necessary information to facilitate the creation of reference files.
For more information refer to the JWST Science Calibration Pipeline documentation.