Gaia Data Release 3 provides novel flux-calibrated low-resolution spectrophotometry for about 220 million sources in the wavelength range 330nm - 1050nm (XP spectra). Synthetic photometry directly tied to a flux in physical units can be obtained from these spectra for any passband fully enclosed in this wavelength range. We describe how synthetic photometry can be obtained from XP spectra, illustrating the performance that can be achieved under a range of different conditions - for example passband width and wavelength range - as well as the limits and the problems affecting it. Existing top-quality photometry can be reproduced within a few per cent over a wide range of magnitudes and colour, for wide and medium bands, and with up to millimag accuracy when synthetic photometry is standardised with respect to these external sources. Some examples of potential scientific application are presented, including the detection of multiple populations in globular clusters, the estimation of metallicity extended to the very metal-poor regime, and the classification of white dwarfs. A catalogue providing standardised photometry for ~220 million sources in several wide bands of widely used photometric systems is provided (Gaia Synthetic Photometry Catalogue; GSPC) as well as a catalogue of $≃ 10^5$ white dwarfs with DA/non-DA classification obtained with a Random Forest algorithm (Gaia Synthetic Photometry Catalogue for White Dwarfs; GSPC-WD).