"Cupping" is the name for the ritualized way that coffee-industry professionals taste beans to rate their quality and take stock of their flavor profiles.
Is there any smell more intoxicating than freshly ground, fresh-roasted coffee? (No. No there's not. Don't argue with me.) Once you get past the initial "warm, fresh coffee" smell, there's a world of aromas going on. Chocolate, nuts, smoke, cherries... What else can your schnoz detect in the grounds?
When wet, the coffee grounds release compounds that might give off surprisingly different smells than when they were dry. This is important because, let's face it—smelling dry grounds is nice and all, but we gotta brew this stuff if we ever want to drink it, and that means we'll be experiencing its aromatic presence while it's in contact with water.
When a cupper pushes the back of his or her spoon through the crust of grounds that formed during the aroma phase, he or she releases a burst of aroma that may give some more clues to the coffee's quality.
Brightness and Flavor
"Brightness" is another way of thinking about a coffee's "acidity," or the fruity characteristics it might have. ("Acidity" in this case has nothing to do with pH, but rather with a certain very valuable type of flavor.) We also often describe this as a coffee's "pop"—the tingle it might give your tongue when you take a first sip. I often try to demystify this to people by suggesting they think of very tingly fruits, such as limes or Granny Smith apples, as compared to not-so-tingly ones, like a cantaloupe or banana.
Meanwhile, flavor itself is pretty self-explanatory: What else does the coffee taste like? (Yes, "coffee" is an appropriate answer as well.) Building a flavor vocabulary can be the hardest part for newbies. We sometimes rely on the Coffee Tasters' Flavor Wheel to help them.
Body and aftertaste are also really important when analyzing a coffee. Body is the tactile feel of the coffee in your mouth. When leading new cuppers through the process, my colleagues and I will often tell them to think about how both whole and skim milk taste recognizably like "milk," but they have sensations on your tongue. "Creamy," "juicy," and tea-like" are common descriptors here, as are the simpler "heavy" or "light."
As for aftertaste, (not afterthought), it's actually a pretty pivotal thing to recognize and rate in coffee. No matter how delicious a coffee might be while you have it in your mouth, if it leaves you with an unpleasant taste once it's down the hatch, that's what you'll likely remember most. In a cupping, we look for the aftertaste's duration, texture, and prominent flavor characteristics.