Contrary to popular belief, Final Fantasy III (Japanese) was not just a prototype for FFV with weaker programming. It is best known for the complex and distinct job system (repeated in FFV) that can be built over your standard "Onion Kids" and changed at the player's will. They key to the job system is "capacity," which is a set of points awarded after each battle like AP in later games; capacity points allow the player to set or change each character's "job." Job options are awarded when your characters free each crystal from the monsters.

FFIII has a key role in the Final Fantasy series as a sort of point of important milestones. It is the last Final Fantasy game released on the original Famicom (1990, by Squaresoft), but it sets a precedent for the following games on the SNES: its basic plot, which involves rescuing elemental crystals from evil minions, is more or less repeated in the next two games in the series (Note the distinction between this plot and the plot of FF1, in which you revive the power of orbs you already posess). FF3j marks the first appearance of Moogles, the Fat Chocobo, and summon magic; the characters also have special abilities to match their jobs (e.g. the thief can actually steal). It is also the first FF game programmed well enough so that your characters will never waste their attacks on enemies they already killed; the attacking enemy is marked by a flash; and lost or gained hit points are displayed as numbers above the target's head. The plot of the game is actually rather interesting, especially for the time of its release. I will give you a simplified version of it:

The great sage Noah had died long ago and divided his legacy among his three pupils: to Dorga he left his magic power; to Unne he left control of the Dream World; and to Zande he left life as a human. Zande, too blind to see that his was the most precious gift of all, grew jealous of the other two for their more powerful gifts and decided to take out his rage on the rest of the world. He is now trying to harness the power of the four crystals to disrupt the crucial balance between light and darkness. Meanwhile, the crystals have chosen four light warriors to prevent this overflow of darkness: the onion kids. Some people believe that this game is an actual sequel to the original Final Fantasy because there is a character named Princess Sara; others believe it is a prequel to Secret of Mana because there is an entity that resembles the Mana Tree. However, there is no substantial evidence for these rumors.