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.