That's a really good question, Sherry.
 
The answer seems to be the sulfhydryl (-S-H) groups surrounding the surface
of bacteria and viruses.  The monograph (Davies and Etris, "Development and
Functions of Silver in Water Purification and Disease Control", 1996)
states (paraphrased, to avoid copyright violations):
 
"In its atomic state, silver has the capacity to absorb oxygen, acting as
a catalyst to bring about oxidation.  Atomic (nascent) oxygen absorbed
onto the surface of silver ions in solution will readily react with the
sulfhydryl (-S-H) groups surrounding the surface of bacteria or viruses to
remove the hydrogen atoms (as water).  This causes the sulfur atoms to form
an R-S-S-R bond, thereby blocking respiration, which causes the bacteria to
expire."
 
- Ela
[Posted in FML issue 2561]