The Bard is one of numerous Jobs granted by the Water Crystal. Final Fantasy III is the first game in the series to feature the Bard job. Bards would go on to make on and off appearances, most infamously Edward in the Final Fantasy IV. Bards in general have been an RPG class since the Dungeons & Dragons days, though how serious of a class they were varied between games.
Bards are a quirky job. Much like Scholars, they has a unique weapon type: Harps. Harps are used to play music at the enemy, meaning that they technically count as ranged weapons. The job's abilities are significantly different between versions: In the Famicom version, Bards manipulate ally and enemy stats with the "Cheer" and "Scare" commands, respectively. In the 3D remake and the Pixel Remaster, their signature ability "Sing" appears instead.
Unused text in the 3D remake suggests that the Bard job would have been optional, the result of a sidequest in which a bard in Duster comes to see Refia as his muse.
Sing is the Bard's signature ability in the remake. When using it, the bard sings a song using their harp. The effects of the song depend on the harp used. The effects of the Bard's songs last two turns and the strength of their abilities grows stronger with job levels (although the difference between min and max is 9%).
Sing becomes one of the quirkiest abilities in the game while still being useful. The songs that the bard sings vary depending on the harp that they are holding. This means that you are locked out of using certain songs until the end of the game as well as the bard getting the most use out of the "equipment" menu option, which allows the character to swap out their weapons mid-battle.
Bards are a Dark Knight's best friend. Paeon, the song from the Dream Harp, can restore 10% of the entire party's health: About half of a Dark Knight's Souleater ability. The guide notes that two Bards and two Dark Knights are a viable party and a high leveled Bard can even support three Dark Knights. A Knight and a Devout are also recommended if you don't feel overly confident in the team's security.