The TaiG jailbreak has been confirmed safe by the well known developer Muscle Nerd. This means that the TaiG jailbreak does not appear to install malware or contain any threats to your device. However, there are always minor risks when using any jailbreak tool and you should always perform a back up before jailbreaking any iOS device.
iOS 8.1.1 users should also uncheck the option to install 3K Assistant 1.0.0 (only Cydia is needed) when using the TaiG jailbreak.
You can learn how to jailbreak any iOS device running iOS 8.1.1 by following the instructions posted here.