Terra’s journey in Kingdom Hearts: Birth By Sleep starts out the same as Aqua’s and Ven’s. The night before, all three witness shooting stars, and wish that all three will one day become keyblade masters. Aqua gives each of them star-shaped keychain charms she made herself.
The next day, Terra, Aqua and Ven are all in front of Master Eraqus, who will judge the exams, and Master Xehanort, who’s there to also watch the proceedings. Terra and Aqua are prepared to take the keyblade master examination, and Eraqus mentions he will be judging not only their physical strength, but their strength of heart. (Note: From here on out all possible spoilers will be in white text, and you need to highlight it to see.)
Master Eraqus only allows Terra and Aqua to take the test, though Ven does help participate in an early challenge. In the last challenge, Aqua and Terra must fight against one another, and during the fight Aqua easily wins and players see a glimmer of darkness around Terra. Master Eraqus declares Aqua a keyblade master and determines Terra isn’t ready yet.
Terra goes to Master Xehanort, who is walking from the main building, and asks him what he should do about the darkness that is within him. Xehanort tells him that if he wants to be a strong keyblade master, he should embrace the darkness and use it. Xehanort then disappears suddenly.
Just after Master Xehanort vanishes, Master Eraqus then assigns a mission to Terra and Aqua. The princesses of heart are in danger, Unversed have appeared in all the worlds, and Xehanort has disappeared. He wants Terra to do something about the Unversed, and find out what’s going on. As Terra prepares to leave, Ven comes running out after him, wanting to tag along and say goodbye. Terra equips his armor and transforms his keyblade into a space-bike thing, and takes off.
Terra heads first for Enchanted Dominion, aka the world of Sleeping Beauty. He immediately encounters Unversed, which he easily defeats. He chases the Unversed until he comes upon a massive castle. Malificent is standing outside, and tells her version of what has happened there. As you can probably guess, she of course isn’t the bad guy here. She’s "discovered" everyone else is asleep, and has no clue why. She does mention she met a man who was looking for the light, the sleeping Princess Aurora.
Terra heads into the castle, battling through the Unversed on the way. He finally reaches the top and unlocks the barrier to Princess Aurora’s room. There he discovers the sleeping Princess Aurora and senses the light in her. Malificent appears behind Terra, tells him Princess Aurora is a Princess of Heart. She then possesses Terra and uses him and his keyblade to steal Aurora’s heart. She then gloats over how she was able to use him so easily, and how powerful she is now that she has Princess Aurora’s heart.
Malificent disappears, and the castle shakes due to the power of an Unversed. Terra heads downstairs to the throne room to find a huge, spinning wheel Unversed. Terra fights and defeats it. He laments that he allowed himself to be used and commit such an act, then leaves Enchanted Dominion, and as he does decides that it is far to dangerous to even consider using the darkness within him. Malificent watches him from the castle as he leaves.