Proofing (also called proving) is a step in creating yeast breads and baked goods where the yeast is allowed to leaven the dough. This step is not often explicitly named, and normally shows up in recipes as "Allow dough to rise".
During proofing, yeast converts glucose and other carbohydrates to carbon dioxide gas which gives the bread rise and alcohol which gives it flavour. Bacteria which coexist with the yeast consume this alcohol, producing lactic and acetic acids. Different types of bread have vastly different requirements for proofing depending on their recipe. Some breads will only require a single proofing while others will need multiple periods. Between stages of proofing recipes will often instruct a cook to "punch down" or "deflate" the dough to allow the bubbles of gas which have formed in the dough to deflate without popping (called overproofing). Length of proofing periods can be determined by time or characteristics. Often the "poke method" is used to determine if a bread has risen long enough; if the bread, when poked, springs back immediately it is underproofed and needs more time.
Proofing is divided into a number of different categories including fermentation, proofing, retarding, autolyse. Fermenting is any stage of proofing which is completed prior to the shaping of the bread. Often a third of a bread's rise will occur during this stage. Proofing is the general term for allowing a bread to rise while at room temperature after it has been shaped. Retarding is the stage in which bread is placed into a dough retarder, refrigerator, or other cold environment to slow the activity of the yeast. The retarding stage is rarely found in recipes with commercial yeast but often used in sourdough bread recipes to allow the bread to develop it characteristic flavour. Autolyse is a period of rest allowed for dough to relax. After the initial mixing of flour and water, the dough is allowed to sit. This rest period allows for better absorption of water and allows the gluten and starches to align. Breads made with autolysed dough are easier to form into shapes and have more volume and improved structure.