A tethered jailbreak means that every time the device boots, it has to be tethered, that is to say, cabled to a computer and jailbroken again. Obviously, this is an annoyance, and an untethered jailbreak is the gold standard.
Note: Absinthe 2.0 works only on iOS 5.1.1. Also, note that the term "most" was used above; the Absinthe 2.0 jailbreak does not work on the revised 16 GB iPad 2 (you'll recall that although the iPad 2 that Apple continues to sell would seem to have the same specs as last year's model, it is different, and comes with the device ID iPad2,4).
Although it does not support that device, compatibility is expected added in the future. Those using iPhones can rest assured that the Absinthe 2.0 jailbreak works on all iPhones that support iOS 5.1.1, meaning the iPhone 3GS and later.
The iPod touch third- and fourth-generation models are also supported.
The new jailbreak comes from the same partnership that delivered the Absinthe A5 jailbreak earlier this year. That was the first untethered jailbreak of iOS devices based on Apple's A5 system-on-a-chip (SoC), which included the iPhone 4S and iPad 2.
Users who have already jailbroken devices running iOS 5.1.1 using a tethered jailbreak can remove the tethering requirement by using the Rocky Racoon 5.1.1 Untether package available through Cydia (just search for it).
Those who have been waiting for an untethered jailbreak can download from here; it's actually 2.0.1 as the team released a fix for an issue with hanging:
OS X (Leopard, Snow Leopard, and Lion)
Windows (XP, Vista, and 7)
Note: it's been reported that Absinthe 2.0 will not work if you updated to 5.1.1 over-the-air (OTA); you must restore to 5.1.1 via iTunes first.