Titles in Tales of Graces f are basically what provide your characters with growth, and are probably the most important thing for your characters in the game. Every Title has 5 different things you can learn, by earning SP gained from winning battles or completing Inn Requests. You can learn stat increases, new Artes, and even upgrades to your Artes you already learned; the best thing is that when you unequip that title, you still keep those.
Note that every Title has an added bonus of providing some extra whenever you equip it, but you will lose that bonus when you unequip it. Should you leave a Title equipped after learning all 5 levels, you still earn SP for that Title towards mastery of it; if a Title is mastered, then the equippable effect is increased (it's still lost when you unequip that Title). It is best to keep switching Titles to get the most out of your characters (you can switch them at any time; you don't need to level each one to level 5).