DIAGNOSIS The spark electrode (the little ceramic piece with a metal tip next to the burner) for that specific burner is either cracked, dirty, or misaligned.
FIX Lift the cooktop grates and the burner cap off. You'll see the electrode. First, clean any burnt food debris off the tip with a dry toothbrush. Check that the electrode isn't cracked and that the small wire leading to it is intact. Make sure it's positioned correctly—the spark should jump about 1/8 inch to the burner head. You can gently bend the bracket to adjust it.
IF THAT DIDN'T WORK If it's clean and aligned but still clicking with no ignition, the electrode itself is likely dead and needs replacing. Each burner has its own specific spark module/electrode assembly.
HEADS UP When testing, make sure the burner cap is seated perfectly. If it's off even a little, the spark won't reach. Also, listen closely—if the clicking sound is coming from the control area, not the burner, it's a different switch problem.