An ability is actually related to the skills you can learn using Training Points with your character. Early on, the earliest you can get one is by Level 2-3 (if we factor it giving 1 pt per level, or perhaps the first level giving you 2). The reason for this is that one stat needs at least 3 points put into it in order to obtain a skill. Carefully look at whatever may be offered for the character you've selected, rotating between the stats, and check to see what would give you an ability. This would be marked by a different icon from, say, Strength +5 or similar. Once an ability has been learned, the trophy will be given and you will be one step closer to mastering the class for that character, too.