Brakiss was originally sent to Luke's Academy as a spy to learn his techniques in the Force and use them for the Dark Side. Luke was not fooled by Brakiss but allowed him to stay in hopes of turning him to the Light Side of the Force.
For 3 years Brakiss stayed with Luke and learned many things. It was at this time Luke decided he was ready for a test similar to the one he himself took on Dagobah years ago.
Unfortunately, Brakiss did not pass and instead fled from Yavin 4, a broken man. He would return briefly years later under Kueller and years later as the leader of the Shadow Academy which challenged Luke's younger class which included the twins Jaina and Jacen.
The sad tale of Brakiss would come to a tragic end for a Jedi who had so much potential but squandered it in pursuit of the Dark Side.
The backstory of Brakiss was mentioned in Young Jedi Knights but would've been wonderful to hear about an adventure of when he was with Luke at the academy struggling with his identity of which side of the Force he choose to follow. Just one of several ideas which would have made great stories within the Expanded Universe.