[Verizon HTC Droid Incredible 4G LTE] cambunch:
Well, I don't know how much you know about how Android works as a whole, so I am going to try to explain everything.

Are you familiar with Administrator Rights on Windows? Basically, imagine your phone in stock form as a basic user. They can run apps, install them, etc, but they can't really go around making many changes or updating the system. Enter root.

Taken from http://www.linfo.org/root.html:

"root is the user name or account that by default has access to all commands and files on a Linux or other Unix-like operating system. It is also referred to as the root account, root user and the superuser."

So think of root as giving yourself Administator access to your phone. It does this by adding a superuser command (su for short) to the /system partition that other apps can call on for Administrator access to the phone. Normally, if an app tries to change something on the /system partition, Android says "Hey, what are you doing?!? You're not allowed to do that" and doesn't let the app work. When you have the su command, it says "Oh, hey, what's up? Oh you want root access? Well, let me ask the owner...", leading to a UI prompt in which you would grant or deny access to the app requesting root. It would then allow the app to do what it is requesting to do, or not, depending on which option you chose.

With root, you essentially have complete access to the phone OS, and can do anything. Once you are rooted, the next step is usually S-OFF.

S-OFF, or security-off, does just that. It disables any security checks (basically digital file signing/encrytion) when trying to update any part of your phone. This means that files are no longer required to come from HTC and have a digital signature attached to them, but can come from anywhere and it skips the check altogether.

Now, when I say "any part of the phone", I am referring to the entire file structure of the device as a whole instead of just the operating system. I like to describe all the parts like a desktop computer works....

We start with the partitions, which is like having multiple hard drives but really only using one. The /system partition is where the OS is stored. When you download a ROM, this is what you are downloading, a new OS. Sometimes its completely different, like switching from Sense to AOSP. Sometimes it is just has some tweaks included. Either way, it wipes the /system partition and replaces all the files on it. There is also a /data partition where all of your user files are stored, but I won't get into that much here.

Next there is the Kernel. Think of this as your big, all-in-one driver for most of the phone. It tells all the little parts of your phone how to work (CPU, camera, USB port, etc.) with the OS so that everything runs smoothly. The stock kernel is pretty locked down and doesn't like you to tell it to act differently, so we use custom kernels. This lets us tell to CPU to run faster (overclocking), allows our USB ports to accept host mode (attaching a USB drive to the phone, for example), etc.

Then we have the Recovery, which lets us work with the filesystem before we actually boot into it. Think of this like running a repair CD on your desktop. The stock recovery doesn't let us do much, basically just erasing the user data to make the phone just like you pulled it from the box. With a custom recovery, we can make a backup of the entire OS to a folder on the SD card, install files to the OS, erase all the user data, etc. This is where we do most of the "flashing" on the phone by installing .zip files to the /system partition.

This leads us to the Radio, which practically just handles the wireless phone signal. This is what allows your phone to talk to the cell towers and send/receive calls. For the most part we don't mess with this, unless the provider (Verizon in our case) puts out official updates (usually from adding new cell towers), then we can flash them to (hopefully) get better signal quality depending on your area.

Finally (at least for what I'm covering) there is the bootloader. Think of this like the BIOS for your phone. This lets us access the recovery, update the radio, go into fastboot mode, or just boot the phone like normal. All of these options have to be selected before the phone starts booting (once again like the BIOS) as these things aren't accessible from within the OS.

Sooooo, S-OFF lets you access all of those things, you can change any one of them. If you use the HTC Unlock tool, you only get to access to recovery and therefor /system, but nothing else. No changing the kernel, and no (AFAIK) updating the radio. It lets you modify the phone enough for some people, but not completely.

In order to install the 3 button mod, you would need root at bare minimum. It would help to have an unlocked bootloader so that you can flash the file through the custom recovery, but isn't required. But what you really want is S-OFF, as it gives you complete access to the phone, and unlike the HTC unlock, is usually reversible if you ever need to travel down the warranty-claim road.