Tethered or Untethered JailbreakHere I'm going to layout the difference of, and what you shoot for, Tethered or Untethered Jailbreak
Untethered - An untethered jailbreak is a type of jailbreak where your device does not require you to reboot with a connection to an external device capable of executing commands on the device.
Tethered - Tethered means being basically "attached" to your computer in a way; you must boot your device by running code on it (via the dock connector) to make use of an exploit.
Semi Tethered - In some circumstances, a tethered jailbreak can be made "semi-tethered." When a device is "semi-tethered," it can run most applications properly. However, some parts will refuse to operate as expected.
DISCLAIMERREAD THIS BEFORE YOU USE TUTORIAL!
WARNING: I WILL NOT BE HELD RESPONSIBLE FOR ANYTHING YOU CHOSE TO DO AFTER READING THIS INFORMATION. ALL INFORMATION IS FOR ENTERTAINMENT PURPOSES ONLY AND SHOULD NOT BE CONSTRUED AS ADVICE. CONTINUE WITH ANY PROCEDURES LISTED ON HERE AT YOUR OWN RISK. IF YOU ARE NOT WILLING TO ACCEPT THAT THIS WILL EITHER RUIN YOUR WARRANTY OR YOUR IPHONE ALTOGETHER, THEN DO NOT READ ON AND MOST CERTAINLY DO NOT ATTEMPT ANY OF THE PROCEDURES THAT FOLLOW.