Earlier this month, Apple stopped signing iOS 8.4.1, which means that users could not
However, if you have an iPhone 5, iPhone 5s, iPhone 4s, iPad 3 and iPad 2, then there is a working way to downgrade the firmware to iOS 8.4.1.
Command Line Tool DeveloperOdysseusOTA, which allows downgrading the firmware of the iPhone 4S and iPad 2 from iOS 8.xx to iOS 6.1.3, has released a new version of its tool. OdysseusOTA 2 allows you to downgrade iPhone 5, iPhone 5c, iPhone 4S, iPad 3 and iPad 2 to iOS 8.4.1. This tool will allow you to upgrade iOS 7.xx to iOS 8.4.1, instead of updating to the latest version of iOS 9.
Tihmstar, the developer of OdysseusOTA 2, explained how this works:
This works because Apple still signs 8.4.1 OTAblobs for these devices, and we have keys for them. This method does not work on any other version of iOS.
To downgrade firmware, jailbreak is required.
The process of downgrading iOS 9 to iOS 8.4 is presented in detail in the video:
Links to the necessary tools and readme.txt, which has a list of commands, can be found in the video description.