Quoting hell is a catch-all term used to describe the edge places in ircII's quirky syntax where it is not at all obvious just how you're supposed to make something work.
Of course you know by now that in the ircII language, data and code are fully interchangable. When you want to run a piece of code later, the usual way to do this is to pass the code as a string argument to another command that queues it up.
Because arguments to functions are subject to $-expansion and \\-dequoting, sometimes you don't wan the $'s to be expanded at the time you queue up the code (now), but rather when the code is executed (later). Usually you can do this by doubling up $'s and \'ing any characters that have special meanings, such as semicolons.
This is more of an art than a science, and the unpleasant situation of trying to figure out just how many $'s you need to use to get that variable to expand at just the right time is colloquially known as quoting hell.
Let's say you want to output the time. It is the $Z expando.
Let's say you want to output the time in 2 minutes:
timer 120 echo $Z
Oops! That doesn't work, because the language doesn't know that “echo $Z” is code, and it expands all $'s now. You can double up the $ to prevent the expansion from happening until later
timer 120 echo $$Z
Let's say you want to output the time in 2 minutes, but not if the client is doing something like a wait or a redirect.
timer 120 defer echo $$Z
Oops! That doesn't work, because $Z would be expanded at the time that the defer is run, which might be much earlier than the echo. You can double up the $'s again to prevent the expansion at defer-time:
timer 120 echo $$$$Z
This is just a simple example of how crazy it can get. This is by no means the most obtuse example I could come up with.
This document is very much a work-in-progress