Monstrous Moonshine

Via an email alert, I recently came across this question posed in Quora:

Why is 196,884 = 196,883+1 so important?
Can someone explain this in everyday, simple terms?

It was answered by Senia Sheydvasser, P.h.D. Mathematics, Yale University (2017) on Aug 6, 2015 as follows:

Let me sum up the gist of what I wrote here (Senia Sheydvasser's answer to What are some of the most interesting mathematical coincidences?), with emphasis on why this is all so important.

Both 196884 and 196883 were integers that came from important objects in mathematics. 196884 was tied to the j-function, which was important in analytic number theory (speaking roughly: using fancy calculus to answer questions about primes and other integers). 196883, on the other hand, was tied to the Monster group, which was an important object in algebra, specifically in the classification of all finite simple groups. 

Here's the key point: there was no reason to suspect that there was anything at all in common between the j-invariant and the Monster group. They came from completely different fields of study to solve entirely different kinds of problems. And yet... 196884 = 196883 + 1, as John McKay noticed. 

Why were these two integers so close? The initial explanation was that, if you have enough numbers to play around with, you are going to have some coincidences. John McKay was not convinced, and he was right: eventually, people realized that there was deep connection between these two different mathematical fields, which came to be known as monstrous moonshine.

This was the first time I'd heard of the term but it a catchy phrase so I thought I'd investigate further. I came across a video about the topic and I've included it below. The presenter is dreadful but the content involves very high level mathematics and it was way over my head. However, I was familiar with groups and so I thought a good way to approach an understanding would be to first find out more about finite simple groups. Before I go on however, here is the link to the video. 

I choose to revise my understanding of groups by going to Wikipedia, where a wide range of mathematical topics is covered. There is a well-explained and well-illustrated example of a symmetry group that I found helpful. It's a big topic and there's still much to cover but it is still a very active area of mathematical research that impinges on many other disciplines: 

The ubiquity of groups in numerous areas within and outside mathematics makes them a central organizing principle of contemporary mathematics.

I'll keep working my way through this article and hopefully have a better overview of groups at the end of it. Of course, I have numerous text books on the topic that I've collected and to which I can refer to as well if needs be.