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A lot of people recently are confused as to what the difference is between a tethered, untethered, and semi-tethered jailbreak. iOS 4.2.1 is somewhat of a challenge for hackers, but the dark side always wins. This post will easily explain what these three things mean and how they may be important to you.

iOS 4.2.1 is in fact jailbroken, but it is a semi-tethered jailbreak for most newer devices.

Untethered

An untethered jailbreak is where you can reboot your device without having to worry about it not booting up again.

Tethered

A tethered jailbreak means you have to plug your device into your computer and re-run some jailbreaking software to get your iDevice up and running again. Failing to do so will leave your device at the “connect to iTunes” screen.

Semi-tethered

A semi-tethered jailbreak is where you’ll be able to reboot your device without needing a computer, but 99% of jailbreak related hacks, mods, and applications won’t work at all. BUT, sometimes your device may just get stuck at an Apple logo because of some problems with MobileSubstrate extensions. If this is the case, you’ll have to plug your iDevice into your computer and re-run some jailbreaking software to get everything going again.

Currently, the iOS 4.2.1 jailbreak for the iPad, iPhone 4, iPhone 3GS (new-bootrom), iPod Touch 3G/4G/MC is semi-tethered, so you’ll be able to boot it just fine (as long as you aren’t using MobileSubstrate) without the need of a computer.

Source

Note: During 3.1.2 Blackra1n Jailbreak days, iPhone 3GS with new bootroom and iPod Touch MC models are also tethered so this isn't actually a new type of jailbreak.