Proofing is a continuation of the process of yeast fermentation that increases the volume of the shaped dough. Bakers use two terms so they can distinguish between fermentation of the mixed dough and proofing of the made-up product before baking. Proofing temperatures are generally higher than fermentation temperatures.
Underproofing results in poor volume and dense texture. Overproofing results in coarse texture and some loss of flavor.
French bread is generally given a long proof to create its characteristic open texture. Its strong gluten withstands the extra stretching of a long proof.