These are some commonly used comedy terms:
ad-lib - a line that is made up on the spot during scripted material. 
beat - this has two meanings. Either it can be used to describe a section of material (see "bit" below) or mean to take a a pause for some comedic effect. 
behavioral jokes - using non-verbal elements to comedic effect. This often uses emotions, character elements, body language or sound effects. Think of Richard Pryor walking as if he were white, etc. 
bit - this has two meanings. It is a section of material, or a part of a section depending on context. It may also mean an entire self-contained comedic piece with its own purpose.
blue - "dirty jokes". Material with a lot of sexual material, "potty humor" or inappropriate language for its own sake. 
bomb - to fail in a comedic performance.
booker - someone who hires comedians to perform. 
callback - making reference to earlier material. 
capper - the last topper (see below), geared towards getting the biggest laugh. 
catch phrase - phrase designed to be a trade mark, something that the audience will remember the comedian for. 
closer - the final joke in a set. 
creative misunderstanding - a purposeful mistake in the interpretation of an idea for a comedic effect 
dying - similar to bomb, except currently in the process of bombing.
Emcee or MC - introduces the performers and hosts the evening.
gag - a joke.
gag file - a file or journal of jokes to be used in the future or to develop material. 
get it - often used to describe the understanding of a joke.
headliner - the star of a larger show. The "name" that is used to sell an evening of comedy. Usually performs last. 
heckler - someone who interrupts, usually by shouting insults. 
inside joke - a joke targeted to only a few people in an identifiable group. Others would not have the information to "get" the joke.
joke file - a file or journal of jokes to be used in the future or to develop material. 
killing - to perform extremely well. The opposite of dying. 
line-up - a list of pieces to be performed (improv) or the comics set to perform. 
long form - collection of improvised scenes or games based on a single audience input.
LPM or laughs per minute - a theoretical measurement of how quickly the laughs come during a show. The idea being that the more LPM, the better the performance. A set with a low LPM would have to get more tight. 
mic - abbreviation for microphone. 
on the road - traveling to perform. 
one-liner - a quick joke. 
one-nighter - a one night gig. 
open-mic night - a night that allows anyone to get on stage. 
opener - the comedian that is first, or opens the show in a line-up. 
opening line - the first line of a routine. 
POV - point of view. 
premise - the central concept to a routine. 
punch line - the line that is supposed to derive the laughter from the audience. 
regular - local comedian who appears regularly.
reveal - that which exposes the creative misunderstanding or humor. 
running gag - a recurring bit that repeats often during a routine. 
scene - a single location and scenario that two actors perform within.
set - a stand-up comedy routine of any length. 
short-form - a single scene or game performed in an improvisational show based on an audience suggestion.
showcase - a performance offering exposure to its performers (often instead of compensation). 
sketch - a prepared scene for comedic material to be presented in a theatrical setting.
skit - a sketch, but with a slightly less professional connotation.
stage time - the amount of time on stage a performer has. 
tag line - the final line of a comedic setup. Usually a line that leads to the end of a bit and allows the moving on to the next piece.
topical humor - jokes about current events. 
topper - a gag playing off a previous gag. These top one another building on laughter leading to the capper.