Rooting is a way to access the "root" (internal operations) of the phone. Root access allows for other non consumer tasks to be run. Rooting an Android phone is similar to "jail breaking" an iPhone or "unlocking" a Windows Mobile phone.
Pros
Some Pro’s to root an Android phone are:Giving you the ability to almost truly customize the phone just the way you want
Over clock the processor (faster processing speed)
Installing a ROM (or "Mod"), a more updated version of the OS than your phone ships with
Add more home screens From 3 up to 7
Tethering (Wired & Wireless) your 3G or 4G internet connection to a laptop, computer via USB cable, WiFi, or Bluetooth. Making a wifi spot for others to share
Installing themes to your phone
Backing up device data and personal data
You can install any app, even blocked ones.
For older phone O/S, you can use your memory card for newer features that allow you to install and run apps on the memory card (gives you more phone memory).
Cons
There are a few draw-backs to rooting your Phone: If you don’t root properly you may permanently "brick" your phone, making it unusable for anything other than a paperweight
Voiding the manufacturer and service providers warranties.
If the phone needs repair or to be checked by your wireless phone company, you have to un-root or they will not service it and it could also lead to further penalties & such
