After we have a generally understanding of what is jailbreak. It is still necessary for us to further look into tethered jailbreak and untethered jailbreak. Here are the differences between tethered jailbreak and untethered jailbreak.
Tethered jailbreaks are not stable and may be frustrating. A tethered-jailbroken device may cannot boot without computer connection but stop at the Apple logo interface. To power on your device after your it reboots or the battery runs out, you need to connect your device to your computer so that the hardware can make your device "awake" with the help of the jailbreaking tool.
On the contrary, untethered jailbreak refers to that your device stays normal and you can reboot or power on it as it is not jailbroken. Apart from that, you can install a lot of great apps and themes freely and easily with the help of Cydia, the core app every jailbroken iDevice user loves.
Generally, the tethered jailbreak releases before the untethered jailbreak. In most cases, the latest system version can be tethered jailbroken first in contrast with untethered one.