silver sticks very strongly to sulfur, found in parts of proteins. These sulfur groups normally bond to each other in proteins, holding them together and keeping the protein folded up in its correct shape.
But if silver interacts with sulfur then the protein cannot fold correctly, and thus it cannot do its job. Next silver interferes with how bacteria use iron. Iron is often held in the places it is needed by binding to sulfur. And since silver also interacts with sulfur it stops the iron doing so.
Finally, silver causes bacteria to produce extremely toxic substances called reactive oxygen species. These go on to cause damage inside the cell, harming the DNA, proteins and even the membrane that surround cells.
The net result of this silver onslaught is bacteria with severely damaged defences. Most importantly the membranes and walls that surround it are leakier after the silver treatment. Once weakened, they are much more susceptible to conventional antibiotics.