The mode stops internet traffic to and from the app when the drone is being flown. It is likely that DJI was partly motivated to add the feature after the U.S. Army banned DJI drones from its fleet due to possible cyber vulnerabilities. Since Local Data Mode blocks internet access on the DJI app, the location of the user, maps, no-fly-zones and flight restriction zones won’t be detected, meaning users are solely responsible for the flight safety of their drones. Telemetry data, like altitude, distance and speed, will remain stored on the drone even if Local Data Mode is deactivated. The mode is not yet available for iOS or users of the DJI Go 4 app, but is available now for some Android tablets and CrystalSky, DJI’s proprietary drone tablet.
You can read more at the Verge article
However in the fine print it reads: The Local Data Mode feature may not be available in locations where an internet connection is required or highly advisable due to local regulations.… so typical DJI trying to control your drone as much as possible…