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 Courage can be obtained if the player defeats the Grass Sage at Floor 1-5. The Seal of Courage grants you the ability to find random money chests. This is very useful, as money buys gems, which you can combine once you get the Seal of Passion.
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.