The Ranger is one of the jobs granted by the Fire Crystal. The Ranger job makes its formal debut in this game. However, Bow weapons were available in Final Fantasy II and were heavily associated with Maria, and Leila to an extent.
The Ranger is an odd physical attacker in the same way one could consider a Scholar an odd mage. The Ranger largely uses ranged weapons, namely arrows and boomerangs-like weapons. Bows in particular are the Ranger's bread and butter, as later bows are exclusive to the Ranger. Bows in Final Fantasy III consist of two parts: The bow itself and the arrows. Both must be equipped to use the bow. Because the Ranger largely attacks by firing arrows at enemies, they can attack from the backline without penalty, making it a reasonable option.
Using a Ranger is a game of resource management. Arrows in Final Fantasy III are finite and the last thing you want is to go into combat only to be fresh out of arrows. Arrows themselves have different properties: From the Village of the Ancients onward, elemental arrows are available and the next batch of arrows from the Invincible focus on status effects. While the arrows have their own damage values, bows will probably be doing most of the heavy lifting. The arrows also count as "Stabbing" weapons, making them useful against flying enemies that are weak to that weapon type. Still, arrows need to be watched to make sure that the Ranger doesn't run out.
Unless you're playing the Pixel Remaster version. In that version, arrows are infinite.
The 3D remake made a few changes. First, the Ranger's White Magic ability was replaced with a new barrage command. Second, new bows were added to allow the ranger more options so that they can keep up with the party. Interestingly, the Yoichi Arrows were made exclusive to Falgabard, but a new arrow type (the Magic Arrows) were added as a replacement. Third, the ability to switch equipment mid-battle was added, which makes it easier to replace arrows.
In the 3D remake, the Ranger's White Magic capabilities were replaced with this mechanic, where the Ranger rapidfires arrows at enemies.