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.
Devices as old as (or older than) the iPhone 3GS with the old bootrom have known bootrom exploits, so PwnageTool can be leveraged to break the device's chain of trust. Newer devices, which include some iPhone 3GS units, as well as all "MC" model iPod touch 2G units, iPod touch 3G units , iPod touch 4G,iPhone 4 and any subsequently released devices, contain bootroms that close the utilized exploit. Those devices with newer bootroms have 2 more exploit :
1. a bootroom exploit that can jailbreak iPhone 3GS , iPod Touch 3G, 4th gen devices also AppleTV and does not work on ipod touch 2G MC models ,
This was used in Limera1n Jailbreak and soon with Pwnagetool / Sn0wbreeze , Also this is pwned4life jailbreak for Current devices :) Tethered
2. a bootrom exploit called SHAtter , wich works only on 4th gen devices or any future devices with the A4 chip ,
This explit is still a secret and will probably jailbreak the new devices that will be released with new Bootroms :) Also Tethered
All those jailbreaks are made unTetherd using a userland exploit found by comex , that can be patched by Apple in 4.2 .
Star runs on the device itself (not a computer program), so it is completely independent from a computer's operating system.
PwnageTool can only be used on Mac OS X.