If you've never had the chance to play other KH games but want to know the story so far, you can look the plots in Wikipedia. This helped me out a bit. The game takes place between CoM and KHII.
Links:
http://en.wikipedia.org/wiki/Kingdom_Heart...f_Memories#Plot
http://en.wikipedia.org/wiki/Kingdom_Hearts_II#Plot
Links:
http://en.wikipedia.org/wiki/Kingdom_Heart...f_Memories#Plot
http://en.wikipedia.org/wiki/Kingdom_Hearts_II#Plot