Could someone explain this game to me?
Like is it a full blown new final fantasy game like III or V, with it's own story, characters, music and stuff?
Welcome to the thread!
To answer your question, well... yes, sort of.
Brave Exvius is a new Final Fantasy game, in the style of the SNES titles (IV, V, VI). That said, the game plays considerably different from the SNES titles, outside of combat. Combat in FFBE is equivalent to the Wait Mode ATB in these games (everyone acts individually in their team's turn before the opposing team gets their turn). In story and event modes, the player's team always goes first. In arena mode, the team that goes first is randomly chosen at the beginning of each new turn.
There is an original story with original characters. As the game is meant to last for several years, the story is considerably drawn out and may appear to be very slow moving (it at all) at first. As one progresses farther in Story Mode, the story becomes considerably more interesting. Please keep in mind that the story really doesn't begin to really get rolling until four or five islands into the game (Dirnado Isle or Olderion Isle), which can be a considerably long time for a new player. Please bear with the story until then.
The game is belongs to a genre known as gacha, or lottery-style game. In this game, not only are there original characters, but the player also has the be ability to pull characters from other Final Fantasies (both heroes and villains) to join them on their team. This is a major draw of the game. On the flip side, as a lottery-style game, the more desirable or popular characters are often quite hard to obtain, and attempts at pulling for them cost a premium currency (lapis) in the game. A fair amount of lapis given to players over time for various events in the game (Brave Exvius is unusually generous in this regard compared to other games in this genre). Addiitional lapis can be purchased for real-world currency to fund additional activities in the game (refilling energy) or for more attempts at pulling rare units from the slot machine.
Various activities are also inserted into the game from time to time, that offer unique equipments, materia, spells, and so on that are not found in the story mode of the game. These can take the form of a dungeon from another Final Fantasy, an exploration of some kind, or a trial against a powerful boss (which is what everyone in the thread is passionate about at the moment as that is this week's challenge).
In this regard, you could think of this as a single-player MMO, as new content is constantly added to the game weekly and new chapters are being added to the story monthly.
If you want to give the game a try, the community would be more than glad to support you on the way. We are pretty passionate about helping GAF succeed here, each in our own ways.