Range is the distance from which an attack can be launched and successfully affect the target. Most Basic attacks have short range while some Special Attacks have longer range. All Super Moves have unlimited range and work the same, regardless of position.
While characters are normally within reach of each other, there are cases with long-reaching attacks becomes useful.
The Arkham Knight's claim to infamy as he is known for his extremely strong heavy basic attacks that deal massive damage from unlimited range, although it has a very long starting/finishing animation preventing it from being used more than once.
The third hit of Cyborg's heavy combo is ranged and has a slow missile speed; it allows him to repeatedly use his heavy combo for the third hit to knock down his opponent again just as they are getting up, until his opponent hit the opposite side of the arena, which would roughly equal 13 heavy attacks. A Super Move can move both combatants back to the center of the arena.
Many special attacks can be used at a range, while melee ones would miss if used at range. However, it will be difficult to make sure they don't block. Exceptions are ranged Basic-Special combos, such as Wonder Woman's Shield Toss, which can hit opponents mid-air after throwing them back with her heavy combo, or Unblockable attacks such as Deathstroke/Arkham Origins's Point Blank. You may also consider using them regardless if the effects would be worth being blocked, such as s1 power drains (e.g. Lex Luthor's Lance Blast, Nightwing's Ground Sparks).
For the AI, ranged specials are coded differently. If you knock them back at block, they may use a ranged special from afar, but will always move up first to use a melee special. There are a couple caveats though: any special that has a ranged part will be coded as "ranged", even if they are partly melee. Notable examples include Harley Quinn/Animated's Hammer Slam and Static's High Gear, both with melee first halves and ranged second halves. Therefore, knocking them back and then blocking can cause them to use these specials at range and miss some of the hits. Another case is specials that is coded as ranged, but has significantly lower range than the norm. Black Adam's Electric Burst for example; while ranged, its range is short and can miss if knocked back far enough. Superman's Flying Punch is a different example; its range is even shorter but the AI tend to use it only when he is closer to his target, but it can still miss.