Synthetic photometry is the calculation of photometry information from spectroscopy data, i.e., calculating what the magnitude would be through various bands/filters.
The exercise is performed to check theories of stars and observations, and to calibrate the two methods. Ultimately, it can help draw conclusions about what information can be inferred from photometry. Of particular interest is a star's absolute magnitude, useful for stellar distance determination.
Given a working theory relating spectroscopy and photometry, libraries of "synthetic stars", i.e., possible stars based upon the theory, and an observed star can be matched against it to determine probable characteristics of the star.