This movie seems to have been specifically designed to appeal to people who have finished the Final Fantasy 7 video game -- which makes sense considering that it's a direct sequel. FF7 fans will love all of the homages to the music, setting, characters, storyline, and fighting techniques of the game. But for non-fans, much of this will probably just go right over their head. Oh, sure, there's some expository introduction at the beginning of the movie, so to some extent I'm sure non-fans could follow along. But for the most part there is not a lot of plot explanation, and there is practically no introduction for the FF7 characters other than of Cloud and Tifa (I don't even think they mention the names of most of them). Thankfully though, there is a great extra on the DVD which recaps key scenes from the game. So for people who haven't played the game, it makes a nice summary, and can be a refresher for those who haven't played in for a while.
The one thing that will definitely impress the audience -- regardless of your gameplay experience -- is the immense volume of eye candy that abounds in this film. There's a lot of matirx-like fighting (ie, slow-down, speed up, slow down, speed up...), which you may or may not like; but the gravity-defying battles, impossible camera angles, and just gorgeous visuals are sure to make just about anybody stop and gape in awe. The director says (in one of the DVD extras) that they didn't want to limit the film's potential by confining the characters actions to real-world physical laws. Their only rule was basically, if it looks cool then do it.
As far as the movie's storyline, in the beginning the story seems like it has a lot of potential; but after a while it seems to ditch story/character development in favor of over-extended (but really cool) fight scenes. And for some reason the ending fight seems kind of deflated. Sure it's visually climactic, but storywise there isn't enough explanation as to why cloud wins at the end (sorry for the spoiler, but come on, like you didn't already know that was going to happen). Maybe I missed something, but after the fight was over I really expected there to be more. I did like how the very last scene played out though so I guess it wasn't all that bad.
Overall, I'd say that if you have played the game then watch this movie because you'll get a kick out of the game references. If you haven't played it, you'll have to take the story with a grain of salt and just accept that you aren't going to understand everything. If nothing else, you can at least enjoy the eye candy.