Mixing silver nitrate (AgNO$_3$) with table salt (NaCl) results in a chemical reaction called precipitation. The reaction can be represented by the following equation:

AgNO$_3$ + NaCl → AgCl + NaNO$_3$

In this reaction, silver nitrate and sodium chloride exchange ions to form silver chloride (AgCl) and sodium nitrate (NaNO$_3$). Silver chloride is a white, solid compound that is insoluble in water, while sodium nitrate is a soluble compound. As a result, the silver chloride precipitates out of the solution, while the sodium nitrate remains dissolved.

The precipitation of silver chloride can be observed by adding a few drops of silver nitrate solution to a solution of sodium chloride. A white, cloudy precipitate will form immediately. The precipitate can be filtered out of the solution using filter paper, and the remaining solution will contain sodium nitrate.

The reaction between silver nitrate and sodium chloride is an example of a double displacement reaction, in which two compounds exchange ions to form two new compounds. This type of reaction is common in chemistry, and it is often used to produce insoluble compounds.