For those who have forgotten High School chemistry, “mole” a word like “pair” or “dozen” or “score”, in that it refers to a certain number of things. But while “a dozen doughnuts” means twelve doughnuts, “a mole of doughnuts” refers to 6.02×1023 doughnuts (and, of course, a baker’s mole means 602,000,000,000,000,000,000,001 doughnuts).
6.02×1023 is known as Avogadro’s number (which is why you should celebrate Mole Day by having guacamole at lunch), which has the interesting property that that many hydrogen atoms weigh one gram. Oxygen, with 8 protons and 8 neutrons, has an atomic mass of 16 (minus some change), so a mole of oxygen weighs 16 grams.
This makes life easier for chemists. We all know that two hydrogen atoms and one oxygen atom combine to make one water molecule. And likewise, two dozen hydrogens and one dozen oxygens make a dozen water molecules. So two moles of hydrogen and a mole of oxygen make a mole of water.
So naturally, Mole Day is celebrated starting at 6:02 on 10/23 (US notation. Check with your local chemist and setting of $LC_TIME to find out when it’s celebrated in your area.
Update, Oct. 25: Alert reader Anne Wright pointed out a mistake. Fixed.