DIAGNOSIS The thermostat isn't getting 24VAC power from your HVAC system. The C-wire connection is loose or missing.
FIX Turn off power to the furnace at the service switch or breaker. Pull the thermostat off its wall plate. Check the wires. You must have a wire connected to the C terminal on both the wall plate and the furnace control board. If a wire is there, ensure it's snug under the plate terminal screw. If no C wire is present, you need to run one or use a common wire maker kit like the Honeywell C-Wire Power Adapter.
IF THAT DIDN'T WORK The 24VAC transformer in your furnace may have failed. Use a multimeter to check for 24VAC between the R and C terminals at the furnace control board with the power on.
HEADS UP Never connect or disconnect thermostat wires with the furnace power on. You can blow the low-voltage fuse on the control board.