Apple says in a posting on its support website the update fixes an SSL/TLS security bug:
Firmware update 7.7.3 is recommended for all AirPort Extreme and AirPort Time Capsule base stations with 802.11ac. It provides security improvements related to SSL/TLS. Other AirPort base stations do not require this firmware update.
AirPort base station firmware updates are only installed when you open AirPort Utility, select your AirPort base station, and then update it.
Apple says you may have to re-enable Back to my Mac after installing the update.
Image credit: CNET