tvOS 12.1.1 can be downloaded over the air through the Settings app on the Apple TV by going to System -> Software Update. Apple TV owners who have automatic software updates turned on will be upgraded to tvOS 12.1.1 automatically.
As a minor 12.x.x update, tvOS 12.1.1 focuses on bug fixes and under-the-hood performance improvements. No major features were found during the tvOS 12.1.1 beta testing period, and Apple does not provide release notes for tvOS updates, so it's not known what specific bug fixes and improvements are included in the new software.
If any additional information on the content of the tvOS 12.1.1 update becomes available, we'll update this post.
tvOS 12.1.1 follows the tvOS 12 update, which introduced support for higher-quality Dolby Atmos sound, zero sign-on, and new aerial screensavers created in collaboration with the International Space Station.