Characters with this ability do not gain any advantages or disadvantages.
While traversing scenarios, some actions require the player to pass a randomized check that is influenced by the "Luck" stat. Players with the "Lucky" ability will always pass the randomized check. If the action also has other requirements, though, the action will not necessarily be available.
Characters with the "Frugal" ability have a 10% chance to negate the cost of using a skill/item. In the case of items, this means that the item does not lose a use. In the case of skills, this means that the skill will not drain any SP.
Status effects and buffs/debuffs last for a certain amount of turns during combat. Characters that sport the "Vulnerable" ability make the duration of each one turn longer. This can be both a good and a bad thing: the player could inflict a buff on him or herself that increases his or her stats, which would last longer. On the other hand, if the player is knocked out by an enemy, this will also last longer.
"Delicate" characters have a certain risk-reward dynamic when it comes to using skills: each restraint equipped drains 1 SP per turn, but if the character is totally free then he or she will recover 2 SP per turn. Skill users that can avoid restraints serve to gain an increased output of skills, but being restrained can quickly drain all SP.
"Specialized" characters use their Special stats for basic attacks rather than their Physical stats. Some enemies have better Physical Defense than Special Defense, and "Specialized" characters may have an easier time dealing damage. The flipside is also true: some enemies have enhanced Special Defense.
At every action node, "Efficient" characters can perform one more activity than others can. This includes action nodes that generally do not allow players to perform any activities.