You Can No Longer Downgrade From iOS 8.4.1 As Apple Stopped Signing iOS 8.4
According to ipsw.me, a website that provides real-time signing status for iOS firmware files, Apple has stopped signing iOS 8.4 firmware file. This means that users will not be able to downgrade from iOS 8.4.1 to iOS 8.4.
This does not come as a surprise as for the last few years, Apple has used this strategy to stop users from jailbreaking their iPhone. Apple not only releases new software updates, that fixes the vulnerabilities used by the jailbreaks, it also stops signing the older iOS firmware file, which prevents users from downgrading back to the older iOS version that can be jailbroken.
Apple has patched several exploits used by the TaiG jailbreak in iOS 8.4.1, so you cannot use the TaiG jailbreak tool to jailbreak iOS 8.4.1. The recent iOS 8.4.1 jailbreak by Pangu team that was demoed on HackPwn2015 may not be released to the public with iOS 9 just round the corner.
Downgrading is useful in cases where the previous iOS software update can be jailbroken. Some users also prefer to downgrade back to the older version if they face problems after upgrading to the latest iOS software update.
Currently, if you want to install any jailbreak tweaks, you have to be careful, as a bad tweak will force you to restore your device to iOS 8.4.1 and end up losing all the tweaks installed on your device. In addition, you will not be able to jailbreak your device as there are not jailbreak tools for iOS 8.4.1.