What does untethered jailbreak means?

Answer 1

A tethered jailbreak is a jailbreak that must be run every time your device starts. If you restart your device, the jailbreak will no longer be in effect, so you must connect it to your computer and run the jailbreak again.

In contrast, an untethered jailbreak will not stop working on reboot, so only has to be performed once.

It's called "tethered" because your device must be connected to your computer every time it starts: it's tethered to your computer by the USB cable. "Untethered" means that there is no wire tying it down.

Answer 2

Untethered Jailbreak means if you turn the iphone on or off it will start up completely without the need of starting it up with a computer. So basically if you turn off the phone and turn it on again, your iphone will boot back up to the homescreen instead of needing a computer to start it up