Beacons are small computers that run software, or more specifically firmware. Beacon manufacturers write the firmware that uses Bluetooth software libraries to send out iBeacon, Eddystone and/or sensor data advertising.
When a beacon supports over-the-air (OTA) update, it allows that firmware to be updated without physically connecting to the beacon with wires. An app, such as Nordic nRF Toolbox is used to connect to the beacon via Bluetooth and update the software.
In practice, manufacturers rarely update their firmware so whether a beacon supports OTA update or not isn’t usually an issue.
The only beacons that tend to get updated, as a matter of course, are Sensoro beacons, when the user wants to switch between standard Sensoro firmware and Eddystone Standard GATT firmware.