Flash Drive is the term used to explain the learning of new skills. You actually need to perform these in order to learn anything other than the stock commands the characters come equipped with. An early and easy attempt to learn a skill is by using one skill repeatedly. If you see the yellow/orange lightbulb appear on the far right side of the action set-up screen, followed by a percent chance, this is what is known as the Flash Drive. When executing your skills, the Flash Drive has that chance to execute and create a new skill.
This is also related to levels, so the higher your level, the higher a chance of acquiring the skill that is hidden behind the combo. Late in the game, once I actually got through the optional dungeon, most of my characters were in the triple-digits of levels and they had a 100% or greater chance of learning the skill hidden behind what skills were left.