There could be (and have been) millions of words written about why FF7 was so popular.
My take on it is that it was one of the first games to truly showcase what the (then) new generation of games could look like. Prior to that game, many 3D games were still very primitive, and cutscenes were practically unheard of -- and if they did exist, they were usually 2D, drawn graphics. FF7 really blew people away.
The other side of the coin is the marketing effort behind the game. It was really shoved down everyone's throats in the months leading up to its release. That has a lot of do with whether or not a game sells, regardless of quality -- as anyone can see if they look at some of the top sellers recently (Fantastic 4 was #5 for July).
Personally, I hated the game, but saying that is enough to get a horde of angry villagers busting down my door.
As for the previous FF games, they were massive successes. The reason the series is called Final Fantasy is because Square was dying when they made the first game; if it wasn't a huge hit, they wouldn't be around today.