Burners being inherently creative have evolved their own terminology for a variety of things over the years. Some of the more common ones are defined below.
Playa - The dry lake bed where Burning Man is held.
Black Rock City - The temporary city built around the man.
BRC - Abbreviation for Black Rock City.
Moop - Matter Out Of Place. A broad term covering anything from litter to abandoned camp structures. Essentially moop is anything left on the playa that wasn't there before the event.
Birgin - Contraction of Burn Virgin. A first timer. Virgin is also common usage.
Shirt Cocking - Men wearing a tee shirt but no pants. Sometimes called Donald Ducking.
Daisy Ducking - The female version of shirt cocking.
Sparkle Pony - In the default world you would consider them self involved bimbos (of any gender). On the playa they will be the inconsiderate, mooching, annoying, idiots that managed to bring 30 spectacular outfits but no water (or other necessities, such as willingness to help around camp). Typically sparkling clean at all times (because they used up all their camps shower water), they often seem to be of the opinion that they can get by on just their good looks.
DPW - Department Of Public Works. The folks that spend weeks building the infrastructure of BRC , then removing it after the burn.
DMV - Department Of Mutant Vehicles. The folks who regulate vehicles on the playa.
Burnier Than Thou - An attitude adopted by some vets to point out at every possible opportunity how much they contribute (implying they are better than you). Truly insufferable, but encountered on the internet more than at the event.
Poom - Playa On Our Matter. The opposite of moop. The playa dust is invasive and nothing you bring there will ever be 100% free of it - including your soul.
Default World - Essentially everything outside Burning Man.
Decompression - The let down of returning to the default world after the burn. Excruciatingly difficult for some, easy for others.
LEO - Law Enforcement Officer. There are many and from lots of different agencies.
There are many more, but these should be enough to get you started. Should you be interested in more detailed explanations of wish to learn more than these handful of terms, check out Kit O'Connell's Burner Lexicon Here.