For those unfamiliar between the differences, a tethered jailbreak basically means that if you should restart your phone, you will need to have it connected to your computer and use a special software. An untethered jailbreak basically has none of these limitations, making it more ideal for day-to-day use.
That being said, TaiG has warned that some jailbreak tweaks aren’t compatible with iOS 8.3 yet as Jay Freeman (also known as Saurik and also the person behind the Cydia repository) has yet to update the Cydia Substrate/Mobile Substrate. The jailbreak is also only available on Windows computers so OS X users will have to wait for their release.
If this is a jailbreak that you have been waiting for, hit up TaiG’s website for the details. In the meantime if you do plan on jailbreaking, we should warn you to backup all your data on your phone/tablet before proceeding lest something goes wrong.