Within chemistry there is a very important number, known as Avogadro's number. This number, 6.022×1023, is so large that it almost defies human comprehension. As a result, there have been many attempts at finding an adequate analogy to correctly convey the scale of Avogadro's number.
Most of these analogies have the same shortcoming, however, which is that they express this number in other abstract entities that humans have no intuitive conception of. 'The number of millilitres of water on earth', for example, or 'adding hydrogen atoms on a balance every second since the big bang', or various references to the circumference of the sun. While it certainly conveys that Avogadro's number is a really big number, it doesn't really make it any clearer exactly how big of a number Avogadro's number is. I don't have a good feel for how big the circumference of the sun is, nor would I be able to make a good guess how many millilitres of water there would be in the three lakes close to my house, let alone in the oceans.
None of these analogies thus give a realistic sense of the scale of Avogadro's number, even though that's the only purpose such an analogy could have. When making analogies it's important to reference objects or situations that people can picture easily and preferably have hands-on experience with.
I would thus propose the following analogy for Avogadro's number:
First you take the world's largest cargo ship, that has a capacity of 24,000 containers, each measuring a standard 'TEU' of 6,1 meters long, 2,44 meters wide and 2,59 meters high.
Then you imagine that every single one of these containers is filled with grains of rice. This would give you about 3000 billion grains of rice on the whole ship.
Then you multiply this number by the amount of pages in the Library of Congress, which according to their website is about 10 billion. So that for every single grain of rice in that cargo ship, there is a Library of Congress' worth of pages.
This would give us a total of about 3×1023 pages, so we still need at least another cargoship filled with rice's worth of pages in the Library of Congress in order to get close. If after this doubling we then add another few hundred thousand billion, then you have arrived at Avogadro's number.
Now this hopefully gives you some sense of exactly how unimaginable Avogadro's number is.
So what does this number indicate, you may ask? The exact definition of Avogadro's number has changed a number of times throughout the years, but simply put Avogadro's number is the amount of atoms present in twelve grams of carbon, or about enough carbon to fit in the palm of your hand.