Final Destination is a stage that has been in the series since the beginning, although it was exclusive to the 1-Player mode in the original game. Its inclusion in Melee (and the rest of the series afterwards) is when it became a battleground for competitive modes. There isn't much to the stage, as it's just flat, with no hazards and nothing else to get in the way.
What this game brings into the mix is that Final Destination will be the only stage that is available in the For Glory online mode. Another thing is that every other stage in the game will have its own Final Destination-style stage, with all hazards and extra platforms (like on Battlefield) removed.
