Tethered or Untethered Jailbreak

Tethered or Untethered Jailbreak
Here 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.

Source: http://theiphonewiki.com