Basically for getting experience. When you do crafting leves, they give you experience (that helps big time to level up). Triple leves mean you take one craft leve quest, you turn in item to get experience, the npc asks you if you have surplus and he would take it, so you give them items, he gives you exp again, and he asks for more items again, you turn in and get exp. So basically for 1 leve allowance, you get 3 times experience. Now if you hand in High Quality items, you get 3 times more.
Let's say, 1 leve quest give you 10k exp since it's Triple leve quest, you get 30k exp. But since you turn in HQ items, you get 90k exp. 90k exp for 1 leve quest is better than 10k exp leve quest, especially you only get 6 leves per 24 hours.