Here is a list of all the most important things to know about snowboarding and skiing. The freestyle tricks are highlighted.

A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z

Numbers 
50/50 - A rail or box trick where the rider's board or skis are aligned with the feature

A
Alley oop  - 180 degree rotation up a pipe
Air to Fakie - Airing straight out of a vertical transition (halfpipe, quarterpipe) and then re-entering fakie, without a rotation

Apex  - The crest of the turn, the top of the arc
All mountain - A certain type of snowboard designed to be used on the whole mountain
Approach - The run-in to a feature where the rider gains speed and selects tactics for the feature
ATML - Acronym for approach, takeoff, manoeuver and landing. A system used for evaluating a riders performance on a feature
Aft - Moving your weight towards the rear or tail of the snowboard
Alignment - The arrangement of the body over the snowboard

B 
Butter - To skid or slid in a styled fashion, that can be a form of rotation combined with a press of the nose or tail of a board or skis
Backside Boardslide - A rail move where the board is sliding at right angles to the feature and the rider is facing in the direction of travel
Blunt slide - A side hit rail trick where the back foot is placed on the feature in a boardslide position after the front leg passes over the feature
Backside - Relates to a rotation where the rider turns his/her back into a spin

Boardercross - A cross between slalom racing and a freestyle event where a number of snowboarders race against each other on a course containing various obstacles.
Bail - When you mess up your trick and crash big time
Backside Wall - The wall of the pipe facing towards the back of the rider
Base - The bottom of a snowboard or skis
Bevel - The measurement in degrees of the side or base edge of a snowboard or skis
Blind - When a rider lands looking away from the direction of travel
Bonk - To tap the skis or board on a man made or natural feature
Box - A non-snow sliding feature, generally a wide plastic surface and metal coping on the sides
Bank/Berm - A mount of snow that can be used to make a turn

C 
Cab Spin - A switch frontside rotation, preferably initiated off the nose (nollie)
Corked - Describes an off-axis spin
Counter rotation - A movement of the upper body opposite to the direction of rotation of the snowboard and lower body. Sometimes ued to assist spinning

Camber - The amount of distance between the centre of a board and the surface of the board is placed on its base
Carve - To turn the board on its edge without going into a side slip. A very clean line is left in the snow.
Chairlift - The lift which carries you to the top of the mountain for your next run.
Core - The material which forms the core of the board, (wood, foam, fibreclass)
Chatter - When your edge is fighting to grip hard snow
Clean - Refers to the completion of a trick smoothly and with ease
Compression - The feeling of gforce build up in the body as the rider travels up steeper terrain (jump, pipe etc)
Centre of Mass - The point at which the entire mass of the body may be considered to be concentrated. High for kids, lower for adults

D 
Double grab - Grabbing the board twice in one jump or air

Dope - A trick or something that is cool 
Directional - A type of snowboard which is constructed to ride better forwards, as opposed to a twin tip which can be ridden equally well in either direction
Dryslope - A slope covered with artificial material
Drop-in - The beginning of an approach to a park feature. Often called out for inform other riders of your intention to hit a feature
Detune - To dull a portion of the edge near the tip and/or tail of a snowboard and skis to reduce the amount of edge hook up when turning
Dynamic turns - A form of riding where the centre of mass travels along a different path to the snowboard or skis 

E 
Effective edge - The section of the edge in contact with the snow if the board is balanced on its edge and flexed
Extruded Base - A low grade base that does not retain wax. Great for park or urban jib boards
Eurocarve - A carved turn performed low to the snow, with a lot of front foot extension and laid out
Extension - An increase in the length of the joints. Typically results in an increase in the height of the rider

F 
Frontside - Spinning with the riders chest facing in the direction of travel. Right for goofy riders and left for regular riders

Fakie - Riding backwards on your board
Freestyle - Riding focused towards kickers, rails and pipe
Flex - A decrease, shortening of a joint
Fun park - An area with specially designed and maintained freestyle features
Freeride - focusing on piste performance rather than freestyle (jumps, rails etc)  
Freshies - Grabbing some fresh tracks in powder
Feature - A man-made obstacle generally found within a snow park. Kicker, rail etc
Frontside wall - The wall in the pipe facing the chest of the ride
Fall-line - The direction down if you were to drop a ball and let it fall down the slope

G  
Goofy  - Riding with right foot forward
Grind - To slide on a rail or box feature 
Grab - When a rider grabs the board or skis

H 
Half-Cab - A180 degree switch frontside spin rontside rotation

Hard bindings - Designed to hold your hard boots. Great for racing but not brilliant for freestyle
Half-pipe - U-shaped large trench used for freestyle
Hard pack - Compressed snow packed down to form a solid riding surface
Hip - A kicker or jump where the landing is 90 degrees to the take off
Heelside/heeledge - The edge of the board where your heels overhang
Hard boots - Similar to ski boots, used in conjunction with hard bindings
Hucking - throwing yourself off a jump without any particular skill or style
Hit - A jump, pipe air or rail slide, i.e. to ride a feature

I 
Indy - Back hand grabbing between feet on toeside edge

J 
Japan Air - The front hand grabs the toe edge in front of the front foot, and the board is pulled back into a Method
Jibbing - Either flatland or hitting rails, boxes, poles etc

K 
Kicker - Manmade jump that is used to throw the rider up in the air
Knuckle - The transition between the deck or flat top of a feature and the prepared landing zone

L 
Lipslide - A side hit rail trick where the front foot is placed on the feature in a boardslide position after the trailing leg passes over the feature. Variants are backside lipslide (back lip) or frontside slipslide (front lip)

Leash - Safety strap designed to prevent the board becoming detached from the rider
Lateral - Pressure forces acting horizontally across snow surface
Lip - The last few inches of the takeoff or the vert of a half pipe

M 
Melancholy/Melon - A grab with the front hand between feet on heelside
Method - A grab with the front hand near front foot on heelside and the board is pulled back with the knees bent and the board pulled up to the riders back
Mute - A grab with front hand between feet on toeside
Manual - A trick where the rider balances on the tail of the board or skis
Misty Flip - A forward flip with a rotation
MJ - The rider travels on the rail in a 50/50 position but balances on their toe edge

N 
Nose poke - A jump with the extension of front leg until straight
Nollie - A pop off the nose/tips of a board or skis
Nose Slide - A rail trick where the rider balances on the nose in a boardslide position
Nose press - A rider travels on a rail feature in a 50/50 position but is balancing on the nose of the board

Narrow waist - Middle of board is narrow for quick edge-to-edge transfer. More common on alpine race boards
Natural - The most comfortable direction for a skier to spin
Newbie - Someone new to snowboarding
Nose - Front of the snowboard

O 
Ollie - A basic jump on a snowboard using the flex of the board combined with an extension of the body

Off-piste - Anywhere off the marked slope
Over-vert - Describes a pipe wall that has been cut too steep at the top and may overhang the lower wall 

P 
Poma lift - A form of lift that dragged you up the slope
Plate binding - A device to attach hard boots to a snowboard
P-tex - Plastic used for the bases of snowboards
Pop - To extend the legs to help lift the board
Pump - A way in which to gain speed by pushing/extending the legs and driving the board or skis underneath you in the lower section of a transition

Q
Quadratic sidecut - The board sidecut that is made by cutting 4 different geometric circles

R 
Re-tractable ollie - An ollie that does not involve the extension of the body, just lifting the legs up 

Regular - riding with left foot forward
Rail - A non-snow feature generally made out of metal and slimmer than a box 
Ruts - Worn path in snow from previous skiers or boarders
Range of motion - The maximum distance through which a rider a move a part of their entire body in a particular direction
Rocker - A shape of board where the tip and tail is lifted off the ground, looking something like a banana?
Revert - A 180 at the end of a turn to enable a rider to come out switch?

S
Shifty - A no grab leg extension out and away from the body
Stale fish - When you grab the board between your feet with back hand heel side
Straight Air - A rider take air but does not spin

Street style rail - A side hit rail that requires a pop or an ollie on
Slam - A crash or falling over
Soft bindings - Type of binding for soft flexible boots
Spray  - A skidded turn that throws up snow
Slalom - A timed race through close spaced sets of poles or gates 
Slush - wet snow which slows a rider down
Speed check - A rapid skidded turn that is used to reduce speed
Stomp pad - Rubber or foam pad that is stuck between each binding to help stability whilst going up lifts or when putting on your board
Switchstance - The same as fakie or riding backwards
Stance - The binding position on board, width and angles 
Stoked - A person who is very pleased with their performance 
Switch - A rider begins a manoeuvre riding fakie or backwards
Sintered base - A higher grade base material that retains wax better and is more easily repairable
Slopestyle - A type of snowboard competition featuring runs through a snow park
Steeze - The way in which someone dresses or their style of riding
Stepdown - A type of jump where the level of the level of the lip is built higher than the landing
Sketchy - To lose control of your skis or snowboard
Stepup - A type of jump where the lip of the takeoff is lower than the landing zone

T 
Tweak - When grabbing the rider extends a leg or rotates the board or skis away from their original position to add more style

T-bar - A type of lift that drags you up the slope
Toeside/toe edge - The side/edge of a board which your toes overhang
Transition - The curve of a jump, hit or kicker
Traverse - Riding across the slope or fallline 
Tail - The end of the board by your back leg  
Twin tip - A shape of board or skis where the shape of the nose mirrors the shape of the tail

U  

V 
Vert - Vertical section of a half pipe
Variable Snow - Snow that is chopped up and not smooth

W 
wax- product applied to the base of the board to reduce friction, enabling greater speed. Other greats for dryslopes include Back-to-Black and Mr Sheen
waist narrowest part of snowboard when viewed from above 

X  

Y  

Z
Zero Spin - When a skier takes off and lands switch with no rotation 

Additonal Sources

Park and Pipe - PSIA Instructors Guide 2005
Wikipedia
Snowboard Instructors Guide - PSIA 2007