These are things you might hear at BMX tracks, pump tracks, or MTB bike parks. Some BMX'ers ride MTB too, and everyone rides pump tracks.
Class: 20-inch wheel bikes (the rim is actually 16" but with tire it is 20")
Cruiser: Cruising on 24-inch wheel bikes (the rim is actually 20" but with tire it is 24")
Clips: Anything that mechanically secures your foot to the pedal. Clips 99.99% of the time refers to clipless pedals. Clips are clipless because they don't use a toe clip, thus they are clipless.
Flats: A pedal with a flat surface and no mechanical attachment to your shoe.
Gearing: This means to the front and rear gears. If the front is 44 teeth and the rear is 16 it is 44/16.
Gear Ratio: Divide the gearing and get a ratio. This ratio is a quick starting point for tuning your gearing. For teen and adult riders the starting point is 2.75 (44/16=2.75) and for kids about 2.6.
Gear inches, gain ratio, rollout: These are calculated numbers based on gearing, crank length, and tire diameter. They are more accurate for fine tuning.
Spin: Fast cadence.
Mash: Slow cadence.
Think of spinning as a V-12 at 8,000 RPM. Think of mashing as a diesel at 2,000 RPM. Both create power just in different ways.
Manual: Everyone has definitions for what is and isn't a manual. Basically, it's like pumping on one wheel. You lift the front up over the obstacle and push the rear down.
Pumping: Pumping is used to maintain or gain speed over obstacles. The up-down rhythm you use to get your bike across bumps. Both wheels stay on the ground.
Case: Coming up short on a jump. Most of the time casing ends in crashing.
Moto: The race part. In most races there are three motos per rider group. In UCI races motos are also called ‘heats.’
Obstacle: Anything not flat on the track.
Backside: The downward side of an obstacle. Sometimes called downside.
Face: The upward side of an obstacle.
Turn: A turn is a banked corner, sometimes called a berm. They are made of dirt or asphalt. Most BMX tracks have 3 turns. Some have 4.
Double: Two bumps on one obstacle.
Triple: Three bumps on one obstacle.
Gate: Literally a hinged gate. It’s at the starting hill. The gate is where the race starts. There are a few styles of gates, but they all fall forward.
Starting Hill, The Hill: The place where you start. Can’t miss it.
Staging: The area on or near the hill where riders are organized into their motos before loading in the gate.
Holeshot, taking the holeshot: The rider that leads the others down the first straight "took the holeshot."
Pro-section: A big jump. Pro-sections are basically two ramps; jump off one, land on the other. In between the jumps there are crocodiles, piranhas, and cobras.
Rhythm Section: A rhythm section is several rolling bumps (rollers) placed together in a grouping.
Roller: A single low rounded bump.
Step-down: A step down is like going down the stairs.
Step-up: A step up is like going up the stairs.
Tabletop: A tabletop is like a butte in geography. They are great to learn jumping skills on. Everyone likes tables.
Pits: The area around the track where you can find food vendors and have your non-race space. Also, it is where hordes of semi-feral kids rove.