Silver metal is oxidized to silver ion:
Nitrate ion is reduced to nitrogen monoxide:
We add these half equations together to eliminate the electrons:
Is this balanced with respect to mass and charge? If it is not, it cannot be accepted as a representation of chemical (i.e. physical) reality.
While it might seem a little abstract to include electrons as fundamental reactants and products in these redox transfer processes, their use, as a convenient little fiction, allows us to address these types of problems.