Aftercore: The period after defeating the NS/Freeing the King but still hanging around without ascending for some reason. Perhaps you have turns to burn, maybe you want to participate in a clan dungeon like Hobopolis, maybe you want to delve into Fernswarthy's basement. Or maybe you just want to go for a Level 30 trophy.
BM: Bad Moon Path: A path where prior ascensions mean nothing in the sense of skills and familiars and equipment. You get none. If you want some, you have to earn them during the run, and there are several hades-themed elements and certain special adventures found only in BM. The path is unlocked by not making use of ten-leaf clovers. (You can still [use] them to turn them into disassembled clovers, and a couple other certain specific uses, but for the most part they're off limits.)
Creep: Nothing to do with creepy people or those green exploding minecraft guys, this is half the term for power creep, which is your basic "newer stuff is more powerful than old stuff" which is mostly accurate.
ITOM: Item of the Month: Found in Mr. Store in Market Square, the IotM is available for roughly one month, give or take a couple days. You need a Mr. A to get one directly (available for donating $10 or in the mall for around 12.5 million meat in the Mall(at the moment) or ten Uncle Bucks (which are available for $1 or around 1.27 million meat in the Mall.)) What exactly it is varies; sometimes it's equipment, or a familiar, or access to a new area directly, or a book that gives you a skill for zero karma.
KOL Mafia: A popular automatic KoL-playing program, or app (as you young types (who need to get off my lawn) might call it. Now you don't have to play KoL yourself any more, you can let the program play and read all the funny jokes and references instead of you doing it! Helps reduce tedium of doing the same thing over and over and over* again.
NP: No Path: No special challenges, just the vanilla game itself. Useful to play if you are new at the game or if you've spent so long playing challenge paths that you no longer remember which bits were part of challenges and which are plain ol' KoL.
Spading: The name taken from Bartle's Taxonomy of Player Types, Spading means digging away at things learning how the game goes from a player perspective. (Side-plug: [The KoLwiki](kol.coldfront.net/thekolwiki/) has been filled over the years by spading-type players. It might be a little slower to fill these days, but people are still working on it!)
T69: A name that's stuck for the current style of Standard and current challenge path ascensions, in which the things you use have to be from the last two years worth of non-limited content. Things like old IotMs or from one-time events that happened more than two years ago are either not available or not usable during a T69 run.
*and over and over and over