Synthetic photometry is the calculation of photometry information from spectroscopic 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.
The "input" spectrum for producing synthetic photometry can also the results of stellar structure models, either full-blow structure calculations or just a black-body spectrum plus some known spectral features. Software is currently available to carry out all these various functions.