The headlights are bright but the engine only clicks when the key is turned. The most likely cause is

Correct answer to question 64 (Auto & Shop Information): a battery too weak to supply cranking current

Method

Lights draw a few amps and a starter draws hundreds, so a battery can look healthy and still be unable to crank. The click is the starter solenoid engaging without enough current behind it. Corroded terminals or a bad earth strap produce the same symptom.