Repeated clicking from a gas furnace when it tries to fire is the sound of the ignition sequence failing. Modern gas furnaces have a well-defined startup sequence: inducer fan, pressure switch, hot-surface igniter, gas valve, burners light, flame sensor confirms flame. Clicking usually happens at one of three steps.
The ignition attempt itself. If the hot-surface igniter fires but the burners don't light, or if they light and the flame sensor doesn't confirm within a few seconds, the control board shuts the gas off and clicks relays as it retries. Most modern furnaces retry two or three times before locking out. Cause is usually a dirty flame sensor (cleanable with fine steel wool in five minutes), a weak igniter (replacement $80 to $150 part), or a pressure-switch issue.
Relay cycling on the control board. If you hear clicking but no visible ignition attempt, the board may be stuck in a loop — bad pressure switch, bad rollout switch, or a failing board. This is a $250 to $500 repair depending on which component is responsible.
Gas-valve solenoid cycling. Clicking at the gas valve without burner light is usually a failed valve coil or a dirty igniter sensor circuit. Replacement runs $150 to $350.
If clicking is accompanied by a brief whoosh of ignited gas followed by an immediate shutoff, that's almost always a dirty flame sensor — a five-minute clean usually restores full operation.