Fanfiction is written fan-content about a piece of media.
This typically consists of stories written my fans that take place in a fictional universe that they love.
These stories might explore barely touched upon parts of a fictional world's lore, or might explore what might've happened if a certain plot point happened differently, or might explore character dynamics and mentality.
There used to be dozens of different fanfiction websites in the late 90s and early 2000s, during the earlier days of the internet, and while many still do exist, two sites have come to reign supreme above all others, FanFiction.net and Archive of Our Own (AO3).
Though these sites are the largest, they are not the only ones, and you may find that a smaller site fits your interests more. Many fan-communities will also have their own dedicated fanfiction sites that may have content not present on these larger platforms.
As always, I recommend that you do your own exploration to see what appeals most to you.
Fanart is art of a piece of popular media created by fans. I also include fan-animations under this category. While you may already know about some of the larger sites for fanart, such as YouTube, Instagram, Twitter, and Pintrest, here are a few others:
Fangames are games created by fans about a piece of popular media.
These pieces of media may already be games themselves, or they might be movies, TV shows, or books. Anything could get a fangame.
These may be built with entirely unique code, or they may be built of of existing, official code (which is sometimes of "questionable" legality when it comes to copyright, unlike original code. I will not be linking any games that break copyright here).
Here are some websites for fangames and game-content:
Mods
Game mods, or modifications, are edits or additions to existing game code. These can be as simple as bug-fixes or quality-of-life changes, or can be as extreme as adding hours of entirely new content onto a game.
These are different from questionably legal hacks, as many game publishers will open up their game to legal modding with a few restrictions, such as not allowing direct monetization of mods.
Here are two popular websites for mods.
Be careful when downloading mods, as while there are measures in place to detect viruses or other malicious code, some innocent code may simply be poorly made and therefore incompatible with the base-game or may be incompatible with other mods, which can lead to crashes or even data-loss. Also be careful when downloading mods for multiplayer games, as not all servers allow mods, and you may be banned for "hacking", even if that was not your intention.
Original Fan-Games
Not all fan-games or game-content is based off of existing code, and much of it is entirely original. Here is one source for original fan-games: