What is this "penguin apocalypse" of which you speak?
I can't say much about the first one since I wasn't there (I think I joined the forums not long after), but I'll summarize what I know about it.
A long time ago, there was no lower boards. People could also change their names at will during that time. If I recall correctly, penguinofhonor once mentioned that his current name was not his original one. There was only one board, where everything went, Various Nonsense. In that board, there was a thread. I have no knowledge of how the thread started, but it eventually became a thread where people would use penguin avatars. Usual B12 fad. Then things got out of hand. By the end, the thread had jumped around every single board, culminating in the invasion of Announcements. People were impersonating ToadyOne and ThreeToe. There were even plans to spread the penguins to other forums. Toady eventually banned a lot of people, locked name-changing (you have to ask him instead, nowadays) and nuked Various Nonsense, remaking it into the lower boards of today.
In 2012,
a thread appeared. It was about what mental images did you have of other forum members. People mentioned how they saw others as their avatars, and eventually the penguin fad was revived. Once more it started to get out of hand, especially when some bronies appeared and started taunting (in fun, of course, but some people can't seem to handle that) the penguins. The thread was eventually locked, once talk of invading other boards finally appeared. It had nothing to do, however, with the ban on pony discussions, that was something else.
And that, kids, is how it happened. Now get off my lawn.
EDIT: Finally remembered it was called Various Nonsense