AgCl precipitated out of solution because it's insoluble in water.
In this double-displacement reaction, all the states of the reactants are aqueous, meaning, they are dissolved in water. The insoluble precipitate, AgCl, is solid. NaNO3 is aqueous because it's soluble in water.
So, we write the complete ionic equation with the state symbols as:
AgNO3(aq) + NaCl(aq) ---> AgCl(s) + NaNO3(aq)