Fanfiction is the collective term for fictional stories that derive some part of itself (i.e. characters, plot, universe, etc) from a work already in existence, written by that particular work's fans. Fanfiction is often dismissed as poorly written material using the characters, setting, and plot of an already-written story to satisfy some self-fulfillment for the writer. Generally, people assume that only obsessive twelve-year-old girls indulge in the activity of reading and writing fanfiction, or fanfics, as they are called, to see two characters get together. However, reading and writing fanfiction can often lead to some unexpected benefits.
Encourages Correct Grammar, Spelling, and Syntax
To write well-received fanfiction, you usually have to write in comprehensible English. Unless the story calls for it, correct grammar and spelling is applied as much and as well as possible, and unless the writer is experimenting with style or trying to affect a certain tone, the fanfic will also generally be written in standard English syntax.
Many people only see the fanfiction filled with spelling and grammar mistakes (My Immortal is one of the most infamous fanfics simply for being so bad) because, in all honesty, those will always be more common than a correctly written one. However, to enter the "fandom favorite" status, something all fanfic writers would love to achieve, the first step is generally to apply the rules of English (or whatever language you happen to be writing in) to your story.
Furthermore, this is encouraged by the "beta" process used quite frequently in the fanfiction world. Sometimes other fanfic writers (or very avid readers the writer trusts) will play editor for another writer and "beta", or edit, a story before he or she publishes it. During this process, most or all grammatical/spelling errors are fixed, as well as characterization and continuity issues. In this environment, the fanfic writer is allowed to make mistakes and learn from them, further cementing his or her academic education by applying it to areas of his or her life, which is proven to be the most effective way to learn.
Interpreting Source Material
Fanfiction is inspired from various forms of media. Sometimes it's from a book; other times it might derive itself from a video game, TV show, or movie. There's even a small section on Fanfiction.net for TV commercials, as odd as that is. However, they all require the writer to become familiar with the original work. In most cases (i.e. stories with plots longer than TV commercials), the writer must be aware of the plot and setting of the story. If it is science fiction or fantasy, he or she has to also keep the mythos in mind while writing (mythos are the certain 'rules' that apply to the world: if there are dragons who can't breathe fire, or vampires that sparkle in the sun, the writer must adhere to these rules if he or she wishes to make the fiction as 'realistic' relative to the source material as possible).
Even if one is writing an AU (short for Alternate Universe), where the canon, or source material, mythos is not necessary, the characters that appear in the work must be as 'in-character' as possible to be particularly good. This means that the writer must observe the various characters he or she will include in the story, taking note of the personalities of the characters, watching for catchphrases or other patterns in speech. They interpret what the character's motivations are and how he or she will react to certain situations. Even understanding the interactions and relationships between various characters is important. (For instance, villains can't suddenly become good friends with the hero without good reason!)
This is generally what happens in original written works, called intertextuality (explained in How to Read Literature Like a Professor). This means that the reader (or viewer or player) views the source material, takes it, twists it, and uses it to create their own work. The only difference is that, while original works do this by alluding to past works to create parallels between their character and another, the fanfiction will put the character in question in situations different from the source material, observing how the character grows. Lev Grossman wrote about this intertextuality in TIME magazine in 2011: "Fanfiction is what literature may look like if it were reinvented from scratch after a nuclear apocalypse by a band of brilliant pop-culture junkies trapped in a sealed bunker. They don't do it for money. That's not what it's about. The writers write it and put it up online just for satisfaction. They're fans, but they're not silent, couchbound consumers of media. The culture talks to them, and they talk back to the culture in its own language."
And really, that's what intertextuality is: a conversation between storytellers. In the case of fanfiction, the writer explore certain areas that the original source either did not have time to do or never thought to explore. Some fics, called "deconstruction fics" may take some tropes or themes of the story and explore them in depth (for example, Neville Longbottom from Harry Potter mentions being thrown from a roof and proving his wizardry by bouncing on the sidewalk; though this produces a comedic effect in the series, a writer might choose to seriously look at the abuse prevalent in that scene and might even highlight the parallels in abuse in the Potter/Dursley and Longbottom households). Other fics act as a continuation of the series, detailing what could happen to the characters after the story is over. Even "shipping fics" - which are the fanfiction most often sneered at for just being a cheesy and bad (worse?) attempt at a Harlequin novel, being fics that focus on the romantic relationship between two characters - have to explore the chemistry between the two characters, paying extra attention to their personalities and how well they might mesh using their motivations and possible parallels in each of their stories. It's communication, from the source to readers, who, instead of simply absorbing the story, choose to "talk back" with their own ideas and thoughts.
Why is this important? The entire point of many literature classes is to interpret different stories and to be able to write an essay about the themes or developments in the story. So maybe fanfiction isn't a traditional essay, but to write a decent fanfic, the writer must have enough knowledge of the plot, setting, and/or characters (and possibly themes and motifs) to write it, and that could easily be changed into essay format. So fanfiction doesn't always come from "literature." Whatever source it comes from, the writers examine it intensely, often drawing from it what professors draw from Shakespearean plays. It doesn't matter that the source is not "refined," but rather that people are taking the time to do this at all.