Most writers of fanfiction are fans of whatever work they're writing for.
This may seem obvious and not significant—why, after all, would it be called "fanfiction" if it were not written by fans?—but it actually has a serious impact on the general storytelling style of fanfiction when compared to original fiction. Fanfiction is, at its most basic, a work of fiction that uses elements from a different preexisting work. This means that most writers of fanfiction will, generally speaking, be very familiar with their subject matter—the lore, the worldbuilding, the characters, and the original plot of the work they're borrowing from—and will expect their audience to be similarly familiar with these elements.
Often, a fanfiction, whether written or in some other medium, will focus on one or more of these elements—typically those that the writer is most interested in. In doing so, fanfiction will often omit important, sometimes even plot-relevant, pieces of information, while moving on under the assumption that the audience, being familiar with the work, will know that information beforehand.
Fanfiction, therefore, tends to have an air of incompleteness to it. What would usually fall to exposition in an original work is often left undone in fanfiction, as the work of explaining the world has already been performed by the preexisting fiction. (In fact, fanfic reviewers and readers alike may frown at any and all of the writer's attempts to explain things that "we already know".) This can be confusing for someone who has never experienced the original work—even if it is, say, merely a spin-off of another show—and is why most fanfiction is rarely viewed outside of the resident fandom for the original work it is based on. Ironically, while fanfic is associated with Purple Prose, this can also create Beige Prose as well, as fans usually assume readers know what characters look like and will skip description for the same reason they skip exposition, unless describing an original character, Crossover character, or something like a Canon Immigrant or Late-Arrival Spoiler that's within the universe of the canon but not instantly familiar to the readers. Or describing their favorite in Purple Prose...note
Now, this all may seem like common sense, but it also explains some of the darker aspects of fanfiction. When a writer of fanfiction spends all his or her time with members of the same fandom, there is a reinforcing effect. Things that would never (well, at least in theory) fly in original fiction due to editors (perfect characters, Character Derailment, etc.) are considered almost pervasive in fanfiction, and Sturgeon's Law is in full motion here.
Ultimately, this leads to the majority of fanworks being full of Wish Fulfillment, Mary Sue characters of all types, and other forms of indulgence that are endemic to amateur fiction, with the added strangeness that it's being done by preexisting characters (Original Characters not withstanding) who may or may not be acting in character. This is why many people have a thorough disdain for fanfiction, and why searching through the refuse for good fiction (the beautiful 10%) can be painful. However, it also means that when you do find the really good stuff, the reward is all the more satisfying.
Now, to introduce more possible confusion, there are those who write "fanfiction" who are not actually fans of the work in question they're writing for. The most common form of this manifests as works by the Hatedom of a work, which often exist solely to bash a character/element of the work in question (not that a fan won't sometimes do the same). Other times, someone who's never even seen or read the original work will write a fan work that's only slightly related to the original source material, taking the basic concepts and creating something more akin to original fiction. Such writers often do this for works in the public domain, and you can find this type of fiction in airports around the world.
To make a note on the concept of a Hatedom, there are a few occasions where a fan will write a fanwork which seems to be bashing the original piece of fiction, or an aspect of it, but without any actual intent in terms of insult:
- The Deconstruction Fic: The Deconstruction Fic is designed to do just that: tear down the original work of fiction, and milk every bit of Fridge Logic (and every shred of idealism) for all its worth, to show what would "really" happen in a more realistic setting. When done by the Hatedom, it will typically be used to show how a work of fiction is nonsense, but a fan could do it as well, perhaps simply for Darker and Edgier / Lighter and Softer points, or maybe just to do something more unique than the average, generic fanwork.
- The Fix Fic: The author doesn't like some aspect of the work. In the hands of either a fan or a hater, this type of fiction will typically result in tons of Character Derailment (and possibly Die for Our Ship) in order to "fix" the work, hence the name.
Needless to say, fan works are a complex form of fiction—like original fiction, of course.