The chemical reaction presented above represents a <em>precipitation reaction</em> where interacts two solutions as a reactants and produce two products. When you want to know if the products remain in solution or precipitate as a solid you could concentrate your attention in the states of the different compounds, represented for subscript of letters in a parenthesis.
In the present exercise the potassium nitrate remains in solution owing to the state are (aq) that means aqueous. Barium sulfate , by contrast, will precipitate out because of its state is (s) that means solid.
In summary, the state of compounds helps recognizing the precipitate in a reaction. For this case, the precipitate is .