The Dragoon is one of jobs bestowed by the Water Crystal.
Dragoons were conceputally introduced in Final Fantasy II as the main soldiers of the Kingdom of Deist which, by the time the game starts, has had its water posioned by the Palamecia Empire. By the time the party reaches Deist, the Dragoons were almost entirely wiped out, leaving a woman and her son, one dying Dragon and a lone Dragoon named Ricard, who had gotten swallowed by Leviathan some time earlier and thus was not poisoned like the rest. In FF2, Ricard was a competent sword user, but the nature of the game meant that he didn't have any particular unique skills.
Final Fantasy III reintroduces Dragoons in a style that fans of the series will find familiar. Dragoons are primarily sky-themed fighters, who wield lances to stab at flying enemies. Dragoons in particular are associated with the Megalopolis of Saronia. In a backstory given in old supplementry material and corroborated in the remake, the kingdom was beset by a monster who was defeated by a knight riding a dragon. Leaping from the dragon, the knight speared the beast and slayed it.
Dragoons would go on to be a staple of the rest of the Nintendo-era Final Fantasy games: Final Fantasy IV would introduce the iconic Kain Highwind, Final Fantasy V would include Dragoon as a job and Final Fantasy VI would feature the Dragoon Boots, allowing most party members to use the Jump ability. Edgar and Mog can use spears, meaning that they can most closely mimic Dragoons. Dragoons also maintain a significance presence in the series through later entries and spinoffs.
The signature Dragoon ability makes its debut: The user jumps into the air and lands the following turn.
The immediate and obvious upshot of this is that the Dragoon is essentially absent until the following turn, meaning that any attacks that would threaten them are of no concern.
Under the hood, Jump's power increases as the Dragoon goes up in levels. Specifically, every 11 levels adds an extra 0.1 to the damage factor, from 1.5 to 2.4. This, combined with job level which is also used in damage calculation, means that Dragoons get stronger as time goes on.
Unlike other jobs, Dragoons don't necessary want to slam the Jump button; For random encounters, it's generally quicker to simply fight through enemies rather than wasting a turn jumping. Likewise, Jump doesn't come into its own until around the 60-70 range when the multipliers reach 2.0. Meanwhile, the rest of the party should be prepared for the Dragoon's jumps. A high-agility character will be able to get an item off before the Dragoon soars and jobs like Knight or Viking can help the remainder of the party weather the damage now being targeted towards them.