Seals are consumable items that will allow your units to promote to advanced Classes or switch to another class or job. The cap stat and skills learned vary from different unit classes in the game so changing classes is an integral part of your characters' growth in the game.
Seals can be acquired as enemy drops, rewards, or can be bought from Rod/ Staff shops from your own castle or other castles. The seals sold from shops are limited in the early chapters but later on after upgrading the shops to LV3, players can buy unlimited number of seals as much as they can afford.
These valuable seals allows a LV10+ base unit to get promoted to one of its two advanced Classes. After promotion, the newly promoted unit's level is reset to LV1 but will retain the stats he/she has before promotion (in exception for the stat bonuses or reductions accrued from the selected advanced class). That said, it's recommended for a base unit to reach the level cap first (LV20) before getting promoted to an advanced class to maximize the stat growth.
Depending in your progress in the story (around Chapter 18 onwards), offspring characters you'll get will have an Offspring Seal in their inventory. These special seals will allow the offspring to change to an advanced class. They'll start with their parent's base class but at max level. Offspring seals functions the same as a master seal but only offspring characters can use them.