If you want to be able to cook fluffy pancakes, all you need to be able to do is follow a good recipe.
But if you want to understand what makes a pancake turn out fluffy, that's where we enter the realm of science. But don't worry. Pancake science is not rocket science.
A fluffy pancake is all about air pockets. Without them, you're just eating crepes.
Fluffiness Begins With Bubbles
Producing these air pockets requires, first, the formation of bubbles in the batter, and second, the solidification of those bubbles.
The formation of the bubbles is caused by the release of gas, which in turn is caused by the fact that you added baking powder to your batter. Baking powder is a chemical leavening agent that, when activated, produces CO2 gas. It's this gas that forms the bubbles.
Activating the baking powder happens in two stages. The first occurs when the ingredients are mixed. The chemicals in the baking powder react when combined with liquid, which triggers an initial release of gas. This first release happens slowly.
A second, bigger burst of gas occurs when the batter is heated. Heat produces a quick burst of bubbles, and that's what really gives pancakes their fluffiness. The higher the heat, the more powerful is the release of gas. (These separate reactions are why baking powder is referred to as "double-acting.")
Now, the bubbles form because of the gluten in the flour you used to make the batter. Glutens are long strands of protein molecules. And as these molecules develop, they become elastic. If you've ever seen the way bread dough stretches, that's the elasticity we're talking about.
In pancake batter, the elasticity of the gluten is what allows the bubbles to form. Like balloons that stretch and expand as they're inflated, so do the little pockets of dough. (This is why you can't make fluffy pancakes with gluten-free flour.)
The Next Step: Heating the Batter
The heat (aka "cooking") is also what brings about the solidification of the bubbles.
When a dollop of batter hits a hot griddle or surface of a skillet, it heats up quickly, which because of the second reaction of your baking powder, quickly forms bubbles in the batter.
Simultaneously, in less time than it takes for the bubbles to pop, the liquid in the batter cooks away in the form of steam, the proteins in the egg coagulate, and those CO2 bubbles solidify into a network of air pockets. This airy interior is what gives a pancake its fluffiness.
Your griddle needs to be hot enough to cause the baking powder to activate quickly, which produces large bubbles and thus more fluffiness. Furthermore, a hot griddle ensures that the batter cooks quickly so that the air pockets hold their shape instead of collapsing. This is important. Too low heat will slow the creation of the bubbles, and also the solidification of the bubbles. In most cases, your target temperature should be 375 F.
Additional Fluffiness Factors
Sugar: Sugar binds with the water in the batter and slows the development of the gluten. That means pancakes with a tablespoon of sugar will be softer, less rubbery, less elastic. Sugar will also aid in browning and give you those crispy edges that no pancake can do without. For best results, dissolve the sugar with the beaten egg.
Salt: Salt also slows the development of the gluten, but it also produces a firmer dough.
Fat: Fat shortens the strands of gluten, causing it to be less elastic. For example, think how crumbly shortbread cookies are. Therefore, substituting cream for milk, say, would lead to a denser, less fluffy pancake.
Viscosity: This is another word for how thick your batter is. If your only liquid is milk, or just milk and egg, your batter will be relatively thin. Thin batter will spread out on the griddle, giving you thin pancakes. Thus thin batter is not compatible with fluffy pancakes. For fluffiness to exist, there must be thickness.
You can produce a thick batter by using less liquid. But in this case, thick will merely lead to heavy, leaden pancakes. The corollary to this is that using more flour will also give you thicker batter, but again, not in a good way. This can happen by accident, though, if you measure your flour incorrectly. (You should weigh your flour, not scoop it.)
On the other hand, if you substitute a thick liquid for a thinner one (or for part of the thinner one), you are on your way to making a thicker batter, but one that will still rise and set.
Example: If a pancake recipe calls for 1 cup of milk, substituting 1/2 cup of plain yogurt for half the milk will produce a thicker batter and a fluffier pancake. The acidity of the yogurt will also boost the chemical reaction of the baking powder, producing still more fluffiness. (The same will happen if you substitute buttermilk for some or all of the milk.)
Be aware that thicker batter will take longer to cook, so you'll want to lower the heat of your griddle about 25 degrees to prevent them from burning.
Be Gentle When You Flip!
One last hint is in order here, especially if you've gone to great lengths to formulate your batter, calibrate the temperature of your griddle and so on. When you flip your pancakes, do it as gently as possible! Flopping them over with a big thwack will burst those bubbles, causing your pancakes to turn out flatter than, well, pancakes.