I am a writer so I know that Fan Fiction is a very large genre. Hell, my first published Wattpad story is a Fan Fiction and I am proud of it. I do look back at it now and kinda regret it is my first but I am proud because it helped me to get out there and find out what people look for in stories. It is kind of like an experiment with characters that you don't have to develop and already know so that you can find out what type of a writer you are as well.
I am 21 and still a hopeless romantic so FanFic is a genre that really lets you get a feel for what type of stories you like, what elements really make people swoon or gets a reaction from them. 50 Shades of Grey was originally a FanFic of Twilight (how it developed into what it is now is beyond me but I loved that because I am a Twi-Hard Fan) but it is something that can help your writing. Because E. L. James based her characters off of character she knew had good qualities and could communicate what she was trying to get across to her audience.
The purpose of FanFic to use characters or universes that another writer has created and to use it (and give the original author credit) and to create a story that you know other people would love to read because you, yourself, are obsessed and in love with it. Most people who write FanFic know almost everything about the cast, characters, story and behind the scenes if they are focusing on the actors rather than the characters. Some are for fun while others will push your imagination to the limit. It is a way for normal people like us unsuccessful writers to improve and have fun along the way.
Take for example, in Supernatural I have a friend who was in love with Castiel so she read tons of FanFic that used the first person POV so that she could use another person to create a universe with the characters she loves and that she is familiar with. Fan Fiction is another way of expressing their fondness towards a certain actor, character, or situation. It is like "What should have happened" for Writers.
Or, if you have ever read Sherlock, I know at least one person in your class asked this question. "Were Sherlock and Watson in a relationship?" If you didn't have that person in your class, I can bet you anything they desperately wanted to point it out. Anyway, that is also another form of self-expression because some believe that Sherlock and Watson were involved with each other, to what extent is scarier in FanFic. It is just a form of expressing "what would have happened" so that our imagination and questions can be answered.
If you followed Pewdiepie and that community in general, there is a legendary video of him and CinnamonToastKen reading FanFic about themselves and if you haven't watched it, I highly recommend it if you want to laugh and know you like FanFic. And if you are more of a Markiplier and Jacksepticeye type of watcher than I can only hope that they make an equally funny video reading their FanFic.