Yeast is a living fungus, Saccharomyces cerevisiae, and it is everywhere in the air. Yeast eats carbohydrates, farts carbon dioxide, pees alcohol, and gets hot.
When making pizza dough and bread, the CO2 is captured in pockets of the "sponge" of wet dough (shown above), a process called leavening (remember, Moses didn't have time to let the bread leaven so they ended up with matzohs, flat crackers). The small amounts of alcohol make the sponge smell like fermenting beer, but it evaporates during the baking process.
There are several different types of yeast. There's yeast for baking, for brewing, for making wine, and for nutrition. For my recipes, I standardize on instant. When you bring it home, store it in the refrigerator, and keep an eye on the expiration date. After a while, the cells die.
Active Dry Yeast (ADY). This is the most popular and it can usually be found in grocery stores. It is live yeast that has been dehydrated into tiny granules and it goes into dormancy. It often comes in convenient small packets. You rarely use a whole packet so I recommend you decant it into a small spice jar with a tight lid. No harm, no foul. It remains viable for up to two years. To use it most people "proof" or "bloom" it by dissolving the granules in warm water with a bit of sugar. When it starts to foam, usually within minutes, they mix it in with the dry ingredients. But if you are lazy like me, you can skip this step. You can just mix it in with the dry ingredients and the slightly warm water. The moisture therein is enough to wake up the cells.
Instant Yeast (a.k.a. Quick Rise Yeast or Fast Rise Yeast). Similar to ADY, but the granules are smaller and more porous and it reproduces faster. It's also much cheaper and lasts longer. Like ADY, it can be mixed right into dry ingredients. If you're substituting ADY for instant or vice versa, they can be used interchangeable in the same amounts. ADY just takes a little longer to get going, so lengthen your proof time if necessary to get your dough nice and puffy.
Fresh Yeast (a.k.a. Cake Yeast or Wet Yeast). Fresh from the factory, you'll find it in the refrigerator of your grocery, and you must use it soon. The expiration date is only about eight weeks after packaging. You can crumble it right into the dough.
Sourdough Yeast. This is wild yeast captured in flour and water. It is usually kept alive in a jar of sponge called "starter" or "mother" at room temperature or in the fridge. You have to feed it to keep it alive and to do that you mix some of the starter with fresh flour and water (generally, you discard or use 80% of the starter and mix the remaining 20% with equal parts flour and water). Sourdough yeast brings more complex flavors to doughs than commercial yeast because there is a greater variety of yeast species in the culture. Whereas commercial yeast consists of strains of Saccharomyces cerevisiae, a sourdough culture may also include yeast species such as S. exiguus and Candida tropicalis. The "sour" in sourdough bread comes not from the yeast but from lactic acid bacteria (LAB) in the sourdough culture. In fact, LAB cells account for most of the flavor in sourdough, outnumbering yeast cells by 100 to one.
Different brands. There are many brands of commercial yeast and manufacturers select from strains that work best for different doughs and baking environments to produce the best flavors and texture. The best, most consistent, and most economical we have tried is SAF Instant Yeast (red label).