Diagnosis
The thermostat is calling for heat (sending 24V to W terminal) but the furnace is not responding. The issue is downstream.
How to Fix It
Check the furnace itself. Is the service switch on? Is the gas valve open? Is the furnace door panel fully closed, engaging the safety switch? Check the condensate drain line on a high-efficiency furnace. If the drain is clogged, a float switch will shut the system down.
If That Didn't Work
The problem may be at the thermostat connection. Turn off furnace power. At the wall plate, ensure the W wire is securely fastened under its terminal screw. A loose wire here breaks the signal.
Heads Up
If you have a standing pilot light system, ensure the pilot is lit. If you have an electronic ignition and hear a clicking but no ignition, you likely have a gas supply or ignition control problem. Call a professional.