Free Play is a certain type of Gameplay. Unlike Story Mode, you can choose any character that you have unlocked. Free Play allows you to do the things you couldn't do in Story Mode. Basically, you can use different characters to finish the game.
You can only play Free Play once you have completed the level in Story Mode.
In Free Play, you can find extended gameplay, such as puzzles, new areas, etc. because of more available Abilities due to different available characters. You will also on be able to find certain Minikits unreachable in Story Mode.
Originally, in Lego Star Wars, Indiana Jones, and other Lego Games, the game would give you a few characters to choose from, and it would give a character for each ability (Midget, Digging, etc.), but in Lego Pirates of the Caribbean, you can choose any unlocked character.