To say that a product is aqueous simply means that the product can dissolve in water. That is: it is soluble in water. To determine if a product can be soluble or not one must know solubility rules for ionic compounds. Most general chemistry textbooks have simplified tables for common ionic compounds, however the link below has some of the basic rules. Any compound which is insoluble will form a precipitate. For example:
AgNO3(aq) + FeCl2(aq) ---> AgCl + Fe(NO3)2 is an example of an ionic double replacement reaction performed with aqueous solutions of silver nitrate and iron (II) chloride.
If one checks the solubility rules one would see that chlorides are all soluble in water except those which are formed with silver. Thus silver chloride is insoluble and will form a solid precipitate. On the other hand, all nitrates are soluble so the iron(II) nitrate will be in aqueous solution.