Here are some of the terms I think are commonly used, “must know”, or are just a shorthand way of referring to an archetype, style, or trope. For more information, check TV Tropes, ANN Encyclopedia’s Lexicon, or Wikipedia.
I may also use Japanese honorifics, so please consult Wikipedia or other sources if you are unfamiliar with them (-san, -senpai, etc.). Note that terms like “onee-san” can be used as an honorific (“Sakura-onee-san”) or a standalone way of referring to someone (“Onii-san”). They may also omit the beginning “o” (“Baa-san”) or used with an honorific like -chan (“Ojii-chan”). As tropes/archetypes, the -san or -sama version is standard depending on the term.
Finally, there are different romanization systems. So “bishoujo” may also be seen as “bishôjo” or “bishojo” elsewhere. I tend to avoid used the special characters version for simplicity’s sake.
Bakappuru – A portmanteau of “baka” and “kappuru” (couple). An overly affectionate pair of lovebirds. Almost always in raburabu [see below] mode, sometimes annoyingly so.
Bentou – Also written as “obentou”. A boxed lunch.
Bishoujo – Beautiful or pretty girl. Bishoujo characters can be leads or side characters and range in personalities from likable good girl to the evil villain.
Bishounen – Beautiful or pretty guy. Like bishoujo characters, a bishounen may be any type of character.
BL – Boys’ Love aka shounen-ai/yaoi.
Boke – Funny man in manzai [see below].
Bunko(ban) – A rereleased manga that contains more pages/chapters than a tankouban.
Genki – Cheerful, energetic. Genki-types are usually overly hyper and optimistic.
Hime – Princess. Also can be used in the “my lady” context.
Ikemen – Good-looking, handsome guy. Generally cooler (hotter-looking) than a bishounen.
Kanzenban – A manga release that is usually larger and includes all colored pages.
Kuudere – Quiet and cold initially until they warm up and become kind. Often initially viewed as emotionless or heartless due to their pragmatism. A kuudere is more likely to be a supporting character than a lead.
Loli – Young girl(s) depicted as cute or attractive. Sometimes used to describe a character who looks like a young girl. Someone obsessed with young girls is described as being a lolicon (loli [lolita] complex). Shotacon is also a type of work starring a shota.
M – Short for “masochist”. Often written as “Do-M” aka “extremely masochistic”. Likes to be in pain (physically or mentally).
Manzai – A comedy style which typically features one person as the tsukkomi (straight man) and the other as the boke (funny man). Often performed in a Kansai accent (think U.S. Southern accent). The tsukkomi may use a harisen (paper fan) or the back of their hand to hit the boke in response to the boke’s ridiculousness.
Megane – Glasses. Often used as as a nickname. As an archetype, megane characters are often the smart, cool, calm, and collected type. However, they may scary behind the lenses.
Moe – Attraction or fetish. People (real or fictional) often have a preferred type, like glasses/megane moe, skirt moe, twintail moe, etc.
Oba(-san) – Literally aunt, but also can refer to a middle-age woman. Often females take it as an insult since they don’t feel that old.
Obaa(-san) – Literally grandmother, but also can refer to an old woman.
Oji(-san) – Literally uncle, but also can refer to a middle-age man. Often males take it as an insult since they don’t feel that old.
Ojii(-san) – Literally grandfather, but also can refer to an old man.
Ojou(-sama) – Literally queen. Ojou-sama types are usually either a perfect onee-san or a female ore-sama.
Omnibus – US term for several manga volumes in one, usually similar to Japanese aizouban or wideban. Usually reserved for rereleasing popular series, but more series are being released directly into 2-in-1 or 3-in-1 formats to reduce publishing cost.
Onee(-san) – Literally older sister. Onee-san types are usually kind, beautiful, almost perfect females.
Ore-sama – An arrogant, haughty way of referring to oneself. Ore-sama types are guys who think they are above everyone else.
Ou(-sama) – Literally king. Sometimes used in school life stories for the ore-sama leader.
Ouji(-sama) – Literally prince. Sometimes used in school life stories to refer to the idol of the campus.
Raburabu – “Love love”, aka “lovey dovey”. The goal for many shoujo heroines.
S – Short for “sadist”. Often written as “Do-S” aka “extremely sadistic”. Likes to inflict (physical or mental) pain on others.
Seiyuu – Japanese for “voice actor/actress”. In Western fandoms, “seiyuu” is often used to refer to the Japanese voice actor/actress in an anime while “voice actor/actress” for the English (or other language) cast member. In Japan, they often use the abbreviation “CV” (character voice).
Shota – Young boy(s) depicted as cute or attractive. Sometimes used to describe a character who looks like a young boy. Someone obsessed with young boys is described as being a shotacon (shota [shoutarou] complex). Shotacon is also a type of work starring a shota.
Tankouban – Typical release for Japanese manga in collected format after magazine serialization. Usually slightly smaller than a standard U.S. volume.
Tezuka’s Star System – Tezuka’s system where characters are basically actors cast into other roles (sometimes typecasted). Helps explain reused character designs. See Wikipedia for more information.
Tsukkomi – Straight man in manzai [see above]. Can be used as a verb: “She did tsukkomi.”
Tsundere – Person who seems mean/standoffish (tsuntsun) but is kind or loving (deredere) on the inside. Often thought of as quick to violence, but this isn’t always the case. A tsundere is just usually not honest about how nice they truly are or how they truly feel about someone.
Yakuza – Japanese mafia.
Yandere – Person who is crazy in love to the point of violence. While tsundere characters are often quick to throw a punch, a yandere is more extreme. They’re much more possessive and prone to dark threats to both their love interest and any rivals. Usually females, although more males have been emerging.
Yankee – Also spelt “yanki”/”yankii”. Delinquents. Common traits and habits include skipping school, being violent, hanging out in gangs, and old-fashioned or messed-up school uniforms.