The sub-events are events that are with characters besides the S-Rank females. They don't have any real benefit other than fleshing out the story more and providing more characterization for side characters and they are pretty neat.
You'll find them when you go to the academy, just select the people right above the one to progress the story until you just get random disciples who keep repeating the same thing.
You'll probably get this one after finishing the third labyrinth if you check them each chapter. There are a ton of them that pop up then.