A very generic RPG
The story is pretty simple. Rag-tag group of heroes join together to prevent a terrible evil from destroying the land. The characters are fairly interesting though, and character design has always been a strong point of the Breath of Fire series. Instead of regular humans as characters, BoF offers up humanoid characters. Tiger people, plants, dragons, and dragon hunters. It would be nice if they were fleshed out a bit more, but they remain interesting enough.
Combat is typical turn based RPG combat and not much strategy needs to be used. There's a few neat things that help keep the game interesting like the Mentor system that allows you to pick an NPC who will augment your stats when you level up. Some will make your strength increase faster, and others will teach you spells, etc. It's interesting but again nothing remarkable.
The graphics are bright and colorful and make for some interesting sights at times. The music on the other hand is kind of bizarre. Almost the entire soundtrack is smooth jazz. Kind of like elevator music. Many Capcom games from this time period suffer from this as well, and makes you wonder if the musical preferences of a top executive influenced the developers.
Experienced RPG fans aren't missing out on anything if they don't play Breath of Fire III. It's actually not a bad game for a beginner to the RPG genre since there's nothing overly complicated about the game, and would make a good introduction to RPGs. However there's just nothing new here or done so well that it warrents a look by experienced fans of the genre.