Rooting a phone is changing the operating system on a cell phone so the user has complete control o the phone. When a phone is rooted the user now has root authority on the phone. Root is the most powerful user in UNIX/Linux and can do anything to computers or phones running UNIX or Linux. You normally have just the ability to run the phone but not work on it at core level. Android runs a special version of Linux. Root in UNIX is more powerful than Administrator in Windows.
Reasons that you might have a phone rooted include greater control of the phone, improved battery life, change to a different carrier than issued the phone, change the user interface, install additional apps or applications, and that you can work at command prompt.
Unrooting a phone is putting a phone back to its default settings. However phones that have been rooted and unrooted, cell providers can still tell they were rooted, and they may not support them.
Unlocking a phone is changing the settings so you can use eh phone on a different carrier, for instance Verizon sold it to you and you want to use it on AT&T.
Jailbreaking is a term that is similar to rooting and is usually used in reference to iPhones where rooting is usually used with Androids. Jailbreaking does not give you full power but will allow using other apps and possibly changing carriers.
Bricks are phones that people tried to root or jailbreak and the process did not work (not often but happens) and the phone is unable to be unrooted or gotten working. Basically all the phone is good for now is a paperweight.
If you decide to have a phone rooted or jailbreaked be aware that this almost always voids the warranty so the company that sold it to you and provides your service will probably not work on it. My intention in this article was to tell people what these terms are that they may hear being used and not to tell them to root or jailbreak them or how to do that. However there are a lot of people who do these to phones and people need to know what the terms are. Just be aware that anytime rooting or jailbreaking is done it is at the phone owners risk.
Rooting can be done on tablets, phones and iPods.
Thanks Evelyn for help with the definitions.