@lasp15 sorry I took so long to respond, but sure!
Fanfiction is any kind of story written by fans that uses the names or locations of the original thing they're fans of using pieces of the original story and lore as building blocks. These can be adapted into their own original stories by changing names and developing more additional lore.
Harry Potter fanfiction is any fanfiction using the original work of Harry Potter, this includes crossovers too, obviously
I'm not sure how to describe the fan culture/fandom of HP fanfic, there's an unfortunately large amount of toxicity and romanticisation of actions and characters that are abhorrent (see Snape for example; a stalker and abuser who created a spell for deadly torture, but the fandom so often sees him as an uwu innocent soft boy because he had an obsession with Lily) and constant flip flopping on important issues like misogyny and biggotry. It is probably a lie to say it's worse than other fandoms though.
The people who write HP fanfiction are the people who want to.
I feel like the HP fandom is old enough you can find bias in almost every direction (though I find there aren't nearly enough who try to portray Snape anywhere near accurate, as well as other completely loyal Death Eaters) and the bias comes more from readers only reading specific parts.
The people who read HP fanfiction are the people who want to, often fans of the films/books who want more content or are disappointed with the original/Rowling.
Honestly I don't have many especially notable HP fanfics. I tend to read a lot and enjoy most that are well written, but I've never been super deep in the community aspect of the fandom for many reasons, and now I'm more interested in other series.