What does it mean when 'Cool On' or 'Heat On' is flashing on the display?

The flashing message means the built-in compressor protection feature is engaged. The thermostat is forcing the compressor to wait a few minutes before restarting to prevent damage. Once the safe wait time has elapsed, the message stops flashing and the compressor turns on automatically. (Page 9)

From the official Honeywell TH5110D Home Programmable Thermostat manual, page 9

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