Simply put - by choosing "Abilities" you are able to select abilities you want your character to execute. Each ability is added to the ATB gauge, and you can add as many abilities as there are available segments. Greyed out abilities cannot be added to the ATB gauge. Once you’ve selected your abilities, the game will provide you with a list of possible targets. Choose one and the game will play out in the order of the commands you have selected.
You can cancel attacks early should you wish to change your role or select another ability. This is a very good trick to learn, especially later in the game when you encounter stronger enemies. Cancelling attacks just as an enemy Staggers for instance, and then switching to a more appropriate role to gain the best advantage during that state, will make for a swifter progression during battle.