A Seal is acquired upon defeating the major Sage of a set of floors (see: the Tower ). They are essential in order to face and defeat the Grand Sage and claim Titan(s). Seals also have an effect throughout the game.
The Seal of Knowledge can be aqcuired when the player defeats the Electric Sage at 3-5. The Seal of Knowledge grants you an option to pick a fourth choice in the hatchery if you don't want the first, second or third egg that you picked.
The Seal of Sanctity can be aquired if the player defeats the Daco Sage at the final floor of Floor Set 6. The Seal of Sanctity grants you an option to pick a third choice in the hatchery if you don't like the second option you made.