When it comes to food, the word “proof” has two completely different definitions. The verb “to proof” is a baking term that describes the action of yeast. Primarily, it is the act of dissolving active dry yeast in water (or another liquid) before incorporating it into dough to ensure that the yeast is alive and kicking, a definition that might have arisen from the need to test yeast and prove that it was active after having been freeze-dried. It is also the act of letting a complete dough (or a dough starter) rise for any period of time.
The second definition of “proof” is not related to baking, but refers to the alcohol content of liquors and wines. The proof of a given liquid varies by law according to where you are, but in the US it is twice the alcohol content (50% alcohol is 100 proof) by volume at 60F/15.5C. In Britain, the measurement is taken at the lower temperature of 51F/10.6C (resulting in a lower proof for a given spirit than the same bottle would have in the US). In the rest of the EU, the measurement is taken at the higher temperature of 68F/20C.
Bonus “proof” trivia: Did you know that the expression “the proof is in the pudding” is a shortened version of “the proof of the pudding is in the eating”? The full phrase essentially means that you won’t know until you try something, which makes a good deal more sense than the shortened version, since you could certainly produce a bad, but good-looking, pudding and not know it because you didn’t bother to taste it.