In chemistry, the double displacement reaction involves two compounds that react like so, where A, B, C, and D are all elements. 

AB + CD --> AD + CB

The two basically switch the compounds they were in; the anion (in the case of ionic compounds) from the first compound bonds with the cation from the second compound and vice versa. Double displacement reactions are usually done in solutions where the compounds are mixed with water. 

Try the following article for some further reading: https://www.khanacademy.org/science/chemistry/chemical-reactions-stoichiome/types-of-chemical-reactions/a/double-replacement-reactions