There is some kind of story involving parallel dimensions and worm holes, which I suppose explains the crystals in some way. (deathbybeta.com)
With no real story involved in this game, it really became dependent on the gameplay itself, Sadly, the gameplay didn't hold much weight either. (averagexboxgamer.com)
By using them in missions, you'll unlock new side stories involving the characters. (blogs.sega.com)