MODIS Surface Reflectance Data State QA Aerosol Quantity field meaning is unclear
Most likely, climatology means there was no retrieval at all.

Bayesian retrievals combine information from an a priori with information from measurements.  When the retrieval fails for whatever reason, or the measurement contains insufficient information, instead of reporting no measurement at all, they copy over information from the a priori and use the flag to indicate that the reported "measurement" is in fact simply the climatology.

For details, see optimal estimation, in particular the book by Rodgers:

Clive D. Rodgers (2000). Inverse Methods for Atmospheric Sounding: Theory and Practice. World Scientific.