Unit Growth

When units win battles, they earn experience points. When they earn enough, they level up.
When they level up, their stats rise.
Each unit has a maximum level. When they reach it, they will not level up anymore.
When you clear a quest, the units that participated will split the unit experience points you earned equally.
If you brought a companion, the companion's portion is deducted from the unit experience point pool.

Units that used limit bursts get a boost to their burst skill levels."
When their burst skill levels rise enough, their burst levels will rise.
Your units' trust gauges may also rise when you clear a quest.

Experience point, burst skill level, level up, and burst level up calculations occur at the Quest Results screen after you clear a quest.
If you give up or get a game over during a quest, you will not be able to keep any experience points or burst skill level rises from that quest.