It works the same way any developer works, it takes the latent image formed in silver halide grains and converts them to metallic silver. Specifically the pheno

It works the same way any developer works, it takes the latent image formed in silver halide grains and converts them to metallic silver. Specifically the phenols in the coffee (tannins here) and the added vitamin c are the developing agents and the sodium bicarbonate reduces the ph enough for them to work. Other phenol containing compounds work, from walnuts to rosemary. There’s nothing special about coffee other than it’s cheap and readily available.