Trainees are a class type exclusive to Fire Emblem Gaiden/Echoes: Shadows of Valentia and Fire Emblem: The Sacred Stones that has multiple promotion stages. These classes have low bases but are able to promote in to most first tier classes by level 10.
In Gaiden, the only Trainee class in the game is the Villager. The class is notable because of its ability to change into almost every other class in the game (male Villagers can promote to Mercenaries, Cavaliers, Archers or Mages, while female Villagers can promote to Cavaliers, Pegasus Knights, Mages or Clerics). In addition, Dread Fighters can promote back into Villagers.
In The Sacred Stones, the classes are Pupil, Journeyman, and Recruit class. In this game, Trainees automatically promote at level 10 before the start of a chapter. If both routes in game has been completed, the classes gain the ability to class change into a Super Trainees.
There was also the 'Probation' class, which was a class that existed in early development of The Sacred Stones and was probably a Trainee type class.