According to Apple's release notes, the update fixes an issue that caused AirPort base stations from appearing in the AirPort Utility when Back to My Mac is enabled. The firmware updates can be installed using the AirPort Utility app for iOS or OS X.
Apple has reportedly stopped development on its AirPort wireless routers, with no new AirPort products planned for release, but the company will continue to offer bug fixes and updates in the near future.
Article Link: Apple Releases Firmware Update 7.7.8 and 7.6.8 for AirPort Base Stations With Back to My Mac Bug Fix