FAQ – I have sometimes stuck at these three terms while searching for jailbreak. Some jailbreaks support tethered Jailbreak which is least preferable and The best one among them is untethered jailbreak.

What’s Tethered jailbreak – Least preferable
Tethered jailbreak means you’ll have to plug your iOS device into your compute everytime it’s rebooted and choose the just tethered boot option from redsn0w. In case you don’t have a computer near you (with redsn0w), your device will be stuck on Apple logo.
What’s Semi-Tethered jailbreak
iOS 5 semi-tethered jailbreak is a kind of jailbreak which allows you to reboot your device without needing to a compute for “Just Tethered Boot” option in redsn0w. Yes, it’s similar to an untethered jailbreak but actually 99% of your jailbreak related apps and tweaks won’t work at all. The semi-tethered jailbreak is made as a protection for you if your device reboots while you’re on the road. It allows you to make the most of important functions but you won’t get back to fully functional state until using redsn0w again, when you get home.
For myself, my device sometimes stuck on Apple logo while I’m on the road because of the tethered jailbreak. That will help you a lot in case you’re facing like these problems.
What’s Untethered jailbreak – The Best One
That’s the jailbreak where you can reboot your device without having to worry about it not booting up again. Hackers are currently working to get untethered jailbreak on iOS 5.