system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5 - Android rooting and IOS Jailbreaking, How does it work? 

I get the general overall concept of it (youre manipulating the current OS to replace it with a customized one) but what are the minor steps inbetween and how does it work. Please use simple crude language and not the lingo. 

I assume a rudimentary amount of Linux knowledge would help in the process of JB or Root to make it go smoother, but I still get lost in all the different software and firmware versions and methods. Can somebody explain in laymens terms of what what exactly goes on when doing either from start to finish?

You have to understand from an outside observer there are just too many "Rom's" and black snow, white snow, red snow, etc. etc. and broken documentation that makes it get really easy to get lost in the shuffle. It's not like they offer classes in college about this kinda thing yet...
gpt
OK so let's start with the *why*. You just bought a phone and you want it to do something the manufacturer didn't enable. If this was a normal machine you could modify the files on the disk to achieve what you want, but things are different on your phone.

On your computer you might have Administrator (root on Linux) privileges which allow you to change *anything* on your machine, including destroying it (deleting system32, for example) either intentionally or not.

Phones run pretty much the same software (some kind of *nix) but this time you don't have total control, so by extension neither do any of the apps you might be able to run on it.

If the phone manufacturers were competent, this is where we'd stop. You want to change the font on your phone but you don't have the privileges, so you can't.

(un)Fortunately, manufacturers aren't perfect. The software they ship phones with might be vulnerable to some attack that allows software to modify things the manufacturer doesn't trust you to modify. This is how rooting works.

All jailbreaks/roots are based on this principle, get code running on the device, then attack the software to allow it to execute with supervisor privileges (i.e. root). The specifics of these attacks vary, but they're basically doing the same thing a virus would want to do, modify system files.

The best example is the jailbreakme PDF attack. This was a PDF file that was carefully crafted to cause code embedded in the PDF to run as the administrator on iPhones, allowing it to install Cydia. This same attack could be used to place a trojan on an iPhone, just by having the target view this PDF, just how malware spreads vid exploits in Flash. This is why manufacturers fix rise bugs as they're found (as well as protecting their own interests in reducing piracy).

As far as all the *sn0ws and \*ra1ns, these are just names for particular exploits that allow control over the phone's system files to install custom software like Cydia.

Android custom ROMs work similarly, they're essentially custom versions of the operating system that are installed on devices. They're a step above roots because they are normally installed by wiping the old system entirely, whereas rooted firmware is normally slightly modified factory default software.