Pre-Promoted is a term used when for a character who is already in a second tier or third tier class when recruited (such as Seth, Titania, and Frederick). Pre-Promoted characters often tend to lose relevance past the early game because in most cases, outside of the fact that they are already pre-promoted, their stats are mediocre in comparison to other units and with promotion it becomes harder to level them up, so they tend to deteriorate in value after you start manually promoting characters which are often stronger. However, there are also some extremely useful pre-promotes that can help out a lot throughout the rest of the game (e.g. Perceval, Seth, Titania, Geitz, Brigid, Pent).
Some games may use a different formula in either EXP gain or the promotion system. For instance, in Fire Emblem: Mystery of the Emblem, EXP gain is not affected by promotion at all. In Fire Emblem: Genealogy of the Holy War does not take the fact that a character is promoted into consideration in regards to EXP gain, and the level is never reset. Most units that don't start off promoted will have to do so at level 20. Fire Emblem: Radiant Dawn has a 3 tier promotion system, so it greatly changes the value of pre-promotes. In fact, almost every character in the game is pre-promoted so not using prepromotes would be a daunting task indeed. In Fire Emblem Awakening, the Second Seal resets the level to 1, and it can also be used to demote a pre-promote to a first tier class. However, due to the way experience gain works, it may not be advisable to use a Second Seal at the highest level possible since even though the level is reset, half of the levels the unit has upon using a Second Seal is then added upon to the reset level, resulting in a level value that is hidden from the player. (e.g. A unit that uses a Second Seal at level 20 is treated as a level 11 unit after the level is reset.) How high the value this hidden level value grows is dependent on the difficulty being played, however.
Generally speaking, some pre-promoted units are often classified into one of two archetypes:
Jagen is a unit who starts fairly strong and typically join near the start of the game when the player's other units are low-leveled. The pre-promoted unit in this case is deceptive. Although they may start out strong, they usually have terrible growth rates and are not worth using past the first half of the game. Examples of those are: Jagen and Marcus in Fire Emblem: The Binding Blade, and Eyvel in Fire Emblem: Thracia 776.
Oifeys are pre-promoted units that start decently strong and have high enough growth rates that they can continue to be useful even in the final chapters of the game. Examples of Oifeys are: Marcus in Fire Emblem: The Blazing Blade, Seth in Fire Emblem: The Sacred Stones, Titania in Fire Emblem: Path of Radiance, Sothe in Fire Emblem: Radiant Dawn, and Frederick in Fire Emblem Awakening.