2.14 describe the experiments to demonstrate that a more reactive halogen will displace a less reactive halogen from a solution of one of its salts

A displacement reaction is basically a reaction where the more reactive element displaces (pushes out) a less reactive element from a compound. For example...

Chlorine is more reactive than iodine (as it is higher up in group 7). Therefore, if you add chlorine water to potassium iodide solution, the chloride will react with the potassium to form potassium chloride (basically, it displaces the iodine). The iodine is displaced from the salt (potassium iodide) and just kind of gets left in the water solution (this turns the solution brown).