If you want to root an Amazon Kindle Fire running software version 6.3 or earlier and you have a Windows PC all you need is the latest Kindle Fire Utility. But if you’re using a Mac, there’s another solution.
It’s called BreakDroid, and the latest version works with Kindle Fire software versions 6.2.2 and 6.3.
BreadkDroid is actually a multi-purpose rooting tool. It can also root the Samsung Galaxy Nexus, Samsung Glaaxy Note, Motorola Droid RAZR, and a number of other phones and tablets that can be rooted using the GingerBreak, psneuter, and zergrush exploits.
Rooting an Android device allows you to access files and settings that are normally protected. This lets you run apps that require access to those files, such as the app backup utility Titanium Backup.
It’s also generally one of the first things you need to do if you want to replace the bootloader or recovery on a phone or tablet so that you can install custom ROMs such as CyanogenMod.