Proofing yeast, means to test the yeast as to whether or not it is "active". If the yeast is not active, you bread or other pastries will not rise. You don't want to go through all the trouble of kneading your bread and then later discovering your bread won't rise.
To proof yeast, simply sprinkle a small amount in warm (room temperature) water and add a little sugar. If the yeast is active, it will begin to form bubbles.