Rooting of a device means getting the root access. It means that you get the developer mode activated for the device. After rooting a device you get the access to make changes in the codes. Moreover, you can add additional features if you want which the manufacturer didn't add in it. Rooting term is generally used in Android devices while we have the similar analogy for Apple devices know as Jailbreaking. Since Android is based on Unix operating system and on it root has the highest level of privileges, so giving your device the same level of privileges in termed as "rooting".
Some of the features of the rooted device is:
Titanium Backup: Using this feature you can permanently delete or hide any app which you are using in your device. For an instance, if you try to delete gmail app from your device in android, your device won't allow you to do it if it is not rooted. The manufacturer will impose restrictions to do it.
Important Note: If you are not very sure about this, please don't root because chances are you may accidentally delete or do something which may be irreplaceable. So take utmost care before rooting. It will void your device's warranty as well, so never root a new device.