From Dragon Quest Wiki
Talent Blossoming is a training method for specific units in Dragon Quest Tact that allows them to get new perks.
Dragon Quest Tact
Introduced in the big Version 2.0 update, Talent Blossoming allows certain units to learn new skills, gain new resistances and get additional stat boosts. As a mechanic, it was introduced to fight power creep, giving new and intersting skills and bonuses to older units that had become outdated.
Perks can be unlocked in a grid, and doing so requires gold, talent points, blossoming twigs and blossoming flowers. Talent points are obtained by participating in any quest, while blossoming twigs and flowers are rewards in The Blossoming Door quests.