Leo says it's possible he might get pwned (hacker speak for "owned" or "hacked"). First of all, Android is an operating system based on Linux created by the Open Handset Alliance. Google has contributed considerably to it, but doesn't own it. One of the things about open software is that the user is allowed to modify or mess with it. The carriers and some handset manufacturers may not like it and may try to thwart it, but it is possible and even encouraged to "root" the device.
"Rooting" means getting administrator access to the phone. Generally, it's best practice with phones to run as a limited user, not as a "super user" or "root". But there are things you can do if you're running as administrator that can't be done as a limited user. It's possible to run programs that require root access, such as Titanium Backup for example.
It's not necessary to root an Android phone or tablet just to access software from somewhere other than Google. That's just a checkbox in security settings. This is different from jailbreaking an iPhone, which is enabling the phone to access apps that aren't in Apple's App Store.
The rooting process is different depending on the device it's being done on. So before rooting any Android device, Leo recommends checking the XDA Developers Forum, and searching for your particular device. Make sure not to go to just any site for this because Leo says that's how a lot of people end up getting "pwned".