What is the difference between a tethered jailbreak and an untethered jailbreak?:
A tethered jailbreak means you cannot boot (turn on the iPod/iPhone) without connecting it to a computer. Untethered means the device jailbreak is independent of computer, and it can boot all by its lonesome self.
Is jailbreaking illegal?
NO, jailbreaking is 100% LEGAL. Although some sources and apps are reportedly illegal, they are not recommended and are not supported by the jailbreakcentral community.