Re: Tethered, semi-tethered, and untethered
A tethered jailbreak means when the jailbreak is applied, the device turning off and on again will render all jailbreak apps/tweaks and some standard apps unusable until you've run a computer program with the device plugged in.
Untethered is the opposite. You can turn the device on and off like normal and the jailbreak stays working.
Semi-tethered is a development by Saurik, the creator of the Cydia store. It allows the device to reboot and use the standard apps that would not work on a tethered jailbreak, but your jailbreak apps/tweaks will still be unusable.