Extra Gain is the process of Characters being enhanced through the Master/Student Relationship, resulting from Character Creation, in which only the Master usually benefits. Extra Gain can take two forms: Boosted stats and learnable spells.
 Stat Boost
The Master gains 10% of the natural stats of his/her Student. If the Master has multiple Students, then for any particular stat, whichever Student has a higher value is the character that supplies the Master with the bonus. For example, if the Master has two students, one having a higher INT stat and the other having a higher ATK stat, the Master will receive 10% of the INT of the first Student while also gaining 10% of the ATK of the second Student. The bonus is calculated every time each Student gains a level. If the Master reincarnates, the bonus will be lost until the Student gains another level. Because of this, if you are trying to benefit from this relationship, you should level the Master first, then the Student. The complete Master/Student stat boost is capped at 28,000 points per stat (112,000 for HP), very minor compared to other boosts available.
 Learning Spells
Whenever the Master stands next to the Student during battle, the Master gains access to all the Spells of the Student. If he/she uses one enough times (at least 5 without Mentors), it will reach level one and will become "learned" by the Master, so that he/she is then able to use it whenever he/she wants.
If you want a particular character to learn some spells, a common tactic is to use him/her to create a pupil that naturally learns certain spells as it gains levels, such as a Skull. For example, let's say you want your Adell to learn Espoir so he can cure other characters' ailments. You'd have him use his Mana to create a Healer. Healers learn Espoir at level 5, so once you level her up, put her next to Adell in battle; he'll have access to Espoir, as well as Shield and Heal, but they'll be at level 0 and he can only cast them while standing adjacent to the Healer. Once he has cast it 5 times (less if you're using Mentors), the spell will have become level 1 and he can use it wherever and whenever he wants, even if you delete the Healer.
Additionally, a character can learn a spell from a Student of one of his/her Students. For example, if Adell makes a Healer and the Healer makes a Fire Skull, Adell can learn Fire. However, it can only be done indirectly, meaning that the first Student must learn it from his/her Student, then the Master can learn it from his/her first Student (e.g., the Healer must learn it from the Fire Skull, then Adell can learn it from the Healer).
Note: This is not the only way for a character to learn a spell that does not naturally come to it. When a character Reincarnates, he/she will retain any spells he/she had from before the Reincarnation, as long as the Inheritance Rate doesn't knock them below level 1.