Short answers, pulled from the story.
The mole, symbol mol, is the SI base unit for amount of substance. One mole equals exactly 6.02214076 elementary entities, which can be atoms, molecules, ions, ion pairs, or other particles. It allows chemists to count and compare vast numbers of particles using laboratory-scale masses.
One mole contains exactly 6.02214076 elementary entities, written out as 602,214,076,000,000,000,000,000, approximately 602 sextillion. This count is the Avogadro number.
The German chemist Wilhelm Ostwald coined the unit Mol in 1894, derived from the German word Molekul, meaning molecule. The English word mole appeared as a translation in 1897.
The mole was made the seventh SI base unit in 1971 by the 14th General Conference on Weights and Measures. Its definition was revised on the 20th of May 2019 to fix the Avogadro number at exactly 6.02214076.
On the 20th of May 2019, following a vote by scientists from more than 60 countries at the CGPM in Versailles, France, the mole was redefined. It is now defined as containing exactly 6.02214076 elementary entities, rather than being tied to the number of atoms in 12 grams of carbon-12.
Mole Day is an informal observance among chemists held on October 23, written 10/23 in the US, running from 6:02 a.m. to 6:02 p.m. The date and time echo the Avogadro number, approximately 6.022 times 10 to the 23rd power.