Among the anime and manga fan communities, as well as their related fan-fiction groups, people tend to use a lot of Japanese words to refer to things that they talk about. Finding out what they all mean is easy, you just ask. If, however, you have no-one you can ask then a page such as this one can be quite handy. I've put together a list of commonly used words and phrases so you know what they are mean when you run into them.
Hai - Yes. Okay. Responding in the affirmative.
Nani? - What?
Hajimemashite - Nice to meet you.
Ja - Later, as in "I'll see you later". Bye.
Sayonara - Goodbye.
Arigato - Thank you.
Kawaii - Cute.
Ne? - Right?. "You like anime, ne?" is "You like anime, right?"
Hentai - Pervert or perverted. Often used to refer to erotic or pornographic material.
Echii - Lewd or suggestive.
Shonen - (Young) boy. Shonen anime is anime for (young) boys.
Shoujo - (Young) girl. Shoujo anime is anime for (young) girls.
Shonen ai - Male homosexuality.
Shoujo ai - Female homosexuality.
Yaoi - Male homosexuality, usually with sexual implication.
Yuri - Female homosexuality, usually with sexual implication. It is also a common girls name meaning 'Lily'.
Fan service - Somewhat echii material or displays of nudity in a non-sexual context. This is often not nesesary to the plot and put in as a 'bonus' to keep the viewers/readers who would not otherwise be interested in the story. It is usually used for comic purposes, and several series have a hot springs (onsen) episode included so they can use it to greater effect.
Tankouban - A collection of manga, like a graphic novel.
OAV / OVA - Original Animated Video / Original Video Animation. These are straight to video anime series. Unlike western ones they are usually of higher quality than TV series but having fewer episodes, around 3 - 8 instead of 13 or 26. They are the step above TV but a step below feature films in terms of visual quality.
Fic - Short for fiction!
WAFF - Warm And Fuzzy Feelings. Feel good fics.
Dark - A fic that is much more depressing than the material it is based on. Usually Dark fics have plenty of angst and heavy themes such as death, suicide etc. Horror stories are usually classified as Dark fics.
Crossover - A fic that uses characters from more than one source and mixes them together.
Mega-crossover - A crossover that uses characters from a lot of different series/films/whatever.
Fusion - A crossover that takes one set of characters out of their world and has them playing parts in another one, often in place of the regular cast members.
Lemon - A fic that contains heavy and/or explicit sexual descriptions. Originated from the hentai anime 'Cream Lemon'. A lot of lemons are just excuses for pornographic sex scenes, very few actually being great fics in their own right, although the good ones are out there. Somewhere.
Lime - A fic with mild sexual description or fan service. Not pornographic but sometimes mildly erotic in parts, and usually better written than lemons.
SI - Self Insertion. The practice of writing yourself into the story. Some authors use their pseudonyms/fan characters while others just use themselves.
Mary Sue - A fan created character who is superior to the rest of the cast. Generally not considered a good thing, self insertions can end up as Mary Sues thanks to the author going on a power trip!