Whenever you complete a quest, your reward will be a jewel (or an upgraded jewel). Jewels are wearable items: each hero can wear a single jewel (and each jewel can be worn by a single hero), which is done using the Ajorn Jewels menu option.
The hero wearing a jewel will get the bonus the jewel provides, for as long as that hero wears it.
Each quest results in a specific jewel. When replaying (and again completing) a quest already completed, the related jewel will be upgraded, and provide a higher bonus to the wearer. The formula for calculating the bonus is: 20 + (Lvl*10)%