It's a small world in deep space after all.
Ten years before Sora became the Keyblade Master, there were three youths who wielded Keyblades under the supervision and tutelage of Eraqus, a Keyblade Master. Kingdom Hearts: Birth by Sleep follows their story after the disappearance of Eraqus' friend and fellow Keyblade Master Xehanort and the appearance of the mysterious Unversed.
At the outset of the game, three youths in the Land of Departure -- Terra, Aqua, and Ventus (called Ven by his friends) -- are preparing to take a test to earn the Mark of Mastery, and thus the title of Keyblade Master. Following the Mark of Mastery test results, Master Eraqus' friend Master Xehanort disappears, whilst a mysterious type of monster called the Unversed appear across the worlds. Whilst Terra is sent out by Eraqus to deal with the threat of the Unversed, Ven is persuaded by Master Xehanort's apprentice Vanitas to set out and follow Terra against Eraqus' wishes. Aqua is later sent out to watch over Terra and simultaneously attempt to return Ven to the Land of Departure.
Kingdom Hearts: Birth by Sleep allows you to play as all three of the youths in their own independent storylines, and whilst not the first Kingdom Hearts to feature multiple playable storylines that overlap one another (this distinction belongs to the dual Sora/Riku storylines of Chain of Memories), Birth by Sleep is the first one that allows you to choose the order in which you play them. Each story is designed as a single experience, an actual full "mini storyline" of its own, but the three plots are designed to complement one another and fill in the gaps of what each character does during the course of their own adventure.