What is root or being rooted mean?

 

What is Rooting?

 

Taken from the Cyanogen Wiki CyanogenMod Wiki

Most carriers "lock" their handsets to discourage customers from taking their handset and moving to another carrier. Carriers also depend on "exclusivity" agreements to encourage users to switch to their plans so they can use a particular handset (e.g., Apple's iPhone on the AT&T network). To use the handset on another carrier's network it would be necessary to "unlock" the handset. This is done with a code based on the IMEI of the handset that can be provided by your carrier or firms on the internet that are slightly more reliable than west African ebay bidders. Unlocking is not possible with CyanogenMod or any other Android replacement.
 

Furthermore, they may impose software limitations to prevent using the handset in a manner that might undercut their voice plans (e.g., Skype, Google Voice), or putting strain on the data network (e.g., tethering, streaming video). The way to get around this is to acquire 'root' (i.e. Administrator) access on the device, so you can install/modify/fix/break anything you want.
 

Rooting directions vary from phone to phone, but a good place to start would be the Android Development forums at XDA-Developers (.com).
 

In and of itself, root only gives you access to secured parts of the phone, just like if you're using using Windows and you have to click that little Run As Administrator prompt. Basically it's a system developed a long while back that keeps the regular day to day operations from being able to have too negative an impact on the rest of the system.

The positive thing about root is everything it then allows you to do further on down the line including custom apps, configurations and even OS'.

What is root?

to "root" your phone essentially means to give yourself superuser access on it. This is like being the highest level of administrator for the device. This allows you to change the interface of your phone. Once your phone is "rooted" you can install custom ROMs (they look alot like themes, just google the name and you'll see plenty of examples). You can also download "rooted only" applications for use on the device.

A "Root" in general is the most basic directory in a system. For instance the Root of your computer most likely is the "C:" drive. Their also happens to be a "Root" of your smartphone, which is what is manipulated in order to achieve a "rooted" phone and its benefits.

 

What is Root or Rooted Mean?

Gaining root access is the equivalent of having admin rights on Windows.
If you didn't root it or purchase it from someone who stated it was rooted, then it isn't.

With root you are able to access and change all files on your device where as when you arent you can only access the ones the manufacturer want.
Root is the Unix/Linux term for administrator. It gives you permissions you do not have normally with the regular user permissions

To answer the question is in linux you have the opportunity to gain super user access through terminal this is exactly what root does gives you permanent access to root directory of your phone meaning you can mod the phone all you want including erase the operating system and brick the phone on the bad side.

To clarify from above: A phone that is NOT rooted can still be modified (you can still make it LOOK different) by using applications like Launcher Pro, for example, and installing Themes. You don't need to root to do this. If your phone is NOT rooted, you can also still access files that are on the SD card and/or on the internal memory, you just can't access _all_ the files on the internal memory. This is an important distinction imho because a complete newb might misunderstand and think he/she needs to root to access any of his/her files.

1. If you Root your phone, you will be able to access files that you are not allowed to access without root. These are usually important system files, which you don't want to touch unless you know what you are doing because you could screw up your phone.

2. If you root your phone you can use certain apps that need to access parts of the Android system that can't be accessed without root, but these are mostly obscure (in the past you had to root to tether your phone to your computer to share your data for internet access, for example, but that is no longer necessary).

3. Rooting lets you delete the bloatware/crapware that often now comes pre-installed by the manufacturers and carriers, and which usually can't be deleted/uninstalled without root.

4. Rooting lets you install custom ROMs. A ROM is like installing a different version of the Android OS with some changes/tweeks to it, like changing the layout and design of the user interface (UI), or so that you can get a newer version of Android on your phone before the manufacturer releases an update (if they ever even do!).

These are the main things accomplished by rooting, and it is important to note that if you attempt to root your phone and don't do it properly, you could "Brick" your phone, which means it becomes inoperable.
the others have given you good info...
but to put it more simple...
rooting is getting access to the ROOT directory of your internal storage. This is how you can get control of all your phone functions that the service carrier has denied you from.