Each character has a set of skills which he learns through levelups. The individual skill sets define which role (damage dealer, healer etc.) the character occupies.
These lists give you an overview about each chcarters skills. This let's you determine in which direction each chracter is heading so you can build you prefered team early on.
In addition to the chracter skills there are some EX-skills which are triggered through your equipped treasure or even treasure combinations. If they are used wisely they can be a great help in difficult battles.