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A precipitation reaction occurs when you mix two ionic compounds in aqueous solution together, and at least one of their products is not soluble, therefore forms a solid and precipitates. That solid is called a precipitate.
Let's say you have NaCl and AgNO. Sodium Chloride separates into Na+ and Cl-; Silver Nitrate separates into Ag+ and NO3-. Besides the NaCl and AgNO3, now they can also form AgCl and NaNO3.
Then, you use solubility rules to determine whether an ionic compound is soluble in water, and therefore whether the mixture will form a precipitate.
By the rules, we see that AgCl is not soluble, and will precipitate, whereas NaNO3 is soluble, so will simply stay Na+ and NO3.
