Being the first Final Fantasy game for the Super Nintendo, Final Fantasy IV featured several technical advancements over the previous incarnations.  The graphical tile set shares some similarity with FF III, but 16-bit graphics and an expanded color palate give the objects more depth.  Everything feels a bit more real.  The added power of the hardware also allowed for two key graphical improvements.  The first is layering, which created better visual effects, filling the screen with fog or smoke, and lending atmosphere to the dungeons and other locations.  The second is Mode 7 graphics.  Mode 7 was an ability that the Super Nintendo had which allowed the background plane to be rotated against another object in a variety of ways.  This was used by the Super Nintendo to create the illusion of a 3D environment with 2D backgrounds.  FF IV uses the effect for airship sequences in the game.  As the airship takes off, the ground literally tilts and shrinks away, creating an appearance of altitude.  Square continued to refine and experiment with these effects in later games for the Super Nintendo.
The real thing that makes FF IV stand out in the series, however, is the battle system.  Final Fantasy IV is the origin of the Active Time Battle System.  In previous games, your characters would line up on one side of the screen, the monsters would take the other side, and you’d take turns hitting each other with swords and magic.  IV introduced a system where the speed at which your characters acted was actually based on their speed stats.  So faster characters wouldn’t just land more blows on their opponents, they acted more often.  This was another break-out moment for the series, and was a key part of the game for years, although players could still set the controls so that monsters would politely wait if you were called away during a fight.
The other unique feature was a five-person party over the previous games’ four.  This is the largest they ever got, and challenged the player with a difficult choice. Like in II and III, players could set characters in the front row to do more physical damage, or the back to boost defense.  But in IV, some slots were reserved for the front, and others for the back, letting the players choose, but preventing them from putting everyone up front or in back.  Again, the player had to familiarize themselves with the characters, and learn their strengths and weaknesses.  Usually this wasn’t particularly difficult with knights up front and wizards in the back.  However, some sections of the game gave you a party that favored one style over the the other, and left you with more vulnerable characters, or with choosing who to stick in the back for a while.
Final Fantasy IV is a game that focused on delivering one story, and challenging players to master it with very little of the customization offered by previous and later installments.  Still, it delivers it so well, and the mechanics are so deep, that it still remains one of my favorites in the series.