Tethered Jailbreake you need a computer to inject and re-run the jail breaking code every time you reboot your phone.
Untether, the Jailbrake code is storage "somewhere" on the iPhone (outside the File system, since it need to run at boot before the OS is actually started) and is able to run from the phone at boot (without the need of a computer).
For the record, every jailbreak needs a Untether exploit and a thether exploit, The first one allow the hacker to access the section of the phone in order to find a way to injet and permanently keep jailbreak code (also knows as untehter jailbreak). We know (based on hacker telling everyone on twitter) that they already broke the boot code so they can access it (that's how the read the keys), now they are working on ways to exploit the code in order to keep it in there after reboot (A.K.A untether) - An extremely oversimplified explanation but I think it will give you an good idea of how it works -
