AgNO$_3$(aq) + NaCl(aq) → AgCl(s) + NaNO$_3$(aq)
In this reaction, silver nitrate and sodium chloride undergo a process called a precipitation reaction. During this reaction, the positively charged silver ions (Ag+) from silver nitrate combine with the negatively charged chloride ions (Cl-) from sodium chloride to form an insoluble compound known as silver chloride (AgCl). AgCl precipitates out of the solution as a white solid.
The resulting solution contains sodium nitrate (NaNO$_3$), which is soluble in water and remains dissolved in the solution.
Overall, the reaction between silver nitrate and salt solutions results in the formation of the white precipitate of silver chloride (AgCl) and the soluble compound sodium nitrate (NaNO$_3$) in the solution.