Today, chemistry students and nerds everywhere celebrate Mole Day with stuffed animals, cakes, t-shirts and a whole lot of puns and bad jokes.
In this case, a mole isn't referring to the cute burrowing mammal, but instead to a fundamental unit of chemistry that was named after an abbreviation for the German word for "molecule." Moles are used to essentially measure the amount of stuff in a certain substance, with the stuff being particles such as atoms and molecules and electrons. Because the atoms and molecules of different substances have different masses (two atoms of gold would have a lot more mass than two atoms of helium), moles are an easy unit to compare just the number of those particles in chemical reactions. Since the mid-20th century, a mole has been defined as the number of atoms in 12 grams of the most common isotope of carbon, the fundamental element of life. That number is 6.02 x 10^23, thus October 23 from 6:02 a.m. to 6:02 p.m. is officially Mole Day.
The earliest known celebration of Mole Day is mentioned in a 1985 article in a science teacher trade journal. Delaware teacher Margaret Christoph, who later went on to win a national teaching award, wrote of how every October 23 she and her students marked the invented holiday with a variety of activities, many of which are still used today in classrooms. These included baking festive cakes by measuring ingredients in moles, inviting professional chemists to speak about their work, demonstrating chemical reactions and decorating classrooms with chemistry-themed ideas.
Inspired by that article, Wisconsin chemistry teacher Maurice Oehler created the National Mole Day Foundation in 1991 to spread the quirkiness of this holiday. The foundation sets an annual theme for Mole Day celebrations (this year's is "Molevengers," as in the Avengers superhero franchise), collects examples of some of the best mole stuffed animals created by students and teachers, and gives awards to members who help further chemistry education and the recognition of Mole Day.
More recent celebrations have added making and eating guacamole to the tradition, playing "cornmole," and making groan-worthy memes. However it's celebrated, Mole Day today still aims to be how Christoph described it 32 years ago—"a way for students to find out that chemistry can be exciting, rewarding and fun."