Proofing yeast is a process of adding dry yeast to warm liquid with a pinch of sugar. The liquid hydrates the yeast to wake it up, and the sugar gives the yeast a food source to begin feeding on. If the yeast is alive, you will start seeing little bubbles and foaming in the mixture. This is a way to make sure the yeast is alive and gives it a jump start so it is very active when it is added into your recipe.
While many recipes call for this step, it is never required. The original form of active dry yeast required the yeast to be hydrated to function properly in a dough. However, these days it is formulated in a way that doesn’t require hydration before adding it to your dough. If your recipe does not call for this step, you can still do it with the following process, prior to mixing your other ingredients, if you want to make sure your yeast is alive.