Sandbox and Virtualized

Can someone please explain what Sandbox and Virtualized mean? I kinda know but need the definitive explanation.

You ask for the impossible (or I am just too lazy to type that much), because they are broad terms, encompassing many things. Four links to get you started, then follow the rabbit down the hole, Alice.

http://en.wikipedia.org/wiki/Sandbox_(computer_security)
http://www.kernelthread.com/publications/security/sandboxing.html
http://en.wikipedia.org/wiki/Virtualization
http://www.vmware.com/virtualization/what-is-virtualization.html