Silver ions react with iron II to form metallic silver and iron III. The reaction proceeds slowly, the mixture needs to be left for several hours at least, and eventually reaches an equilibrium position in which both ions are present in measurable concentrations.
The concentration of silver ions at equilibrium is measured by titration with potassium thiocyanate.
The method described is a microscale titration. You can use normal scale methods but will have to scale up the volumes used.