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.
Dere(-dere) – Sweet. Often used together in other terms (see below), but when used along, think puppy-dog-like, melting feelings.
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.
Kabedon – “Wall pound”. An action where one character (usually a guy) corners another (usually a girl) against a wall with his arms. Generally, it’s supposed to be heart-pounding and accompanied by words like, “I want only you!” or “Don’t go with him!”
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 be 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. Also written sometimes as “moé” to emphasize its pronunciation.
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 thanks to its oversized size in both page count and width. Originally 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 but is kind or loving 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.