If you care about the story, buy this.
Let's go back a little bit to Kingdom Hearts (the first one that came out on Ps2) and try to remember those worlds from there. Come to this one and you'll be seeing mostly the same except for some. Sounds boring, but it has been given a twist in which you are willing to ignore that fact.
358/2 Days is simply Roxas' story and how he ended up in the Begginning of Kingdom Hearts 2 and why he is so important. You find all this out along the way and this only matters if you really care about the story. If you don't, you will be seeing alot of the same, but some of it is different. This game also plays different in which you don't freely roam worlds like in the other games, but you are given a section of that world to roam for the mission you are given to do for the day. Note: You do not play every day that is listed on the title because if you did, this game would take forever. The new panel system is important as you will be channging your stats/items/magic for the mission you will be doing (for example, you may need fire magic, so you place fire panels in the system).
Storywise, you see everything from Roxas' perspective of the Organization and how he feels about being with them. At some point though, something happens that changes his mind. You also see how he progresses in his friendships with Axel and a new member to the Organization Xion (pronounced "Shion"). As much as I don't want to give out spoilers, the reason this game deals with old worlds is to show his understanding of people and feelings, but it also has something to do with someone elses memories. That's why if you have never played the first Kingdom Hearts and/or Chain of Memories, you might be lost on the story here. This game is assuming you have played the games above and know what's going on.
My only possible complaint for this game is the target audience. Some people will feel to old playing this when they see Disney characters involved, but others might see that younger people may not be able to grasp the gameplay as easily as most hardcore gamers will. I will admit that this is a good game, but I probably could've expected more from Square Enix than repeated worlds.