The solenoid may not be activating because the engine is simply in gear. Most outboards have start-in-gear protection that stops you cranking the motor when it is not in neutral. There is also a fuse that protects the electrical circuit that activates the solenoid. If this fuse is blown the solenoid won't activate and therefore click.
PHOTO Dangar Marine Boat Guide
There is a problem with the boat's battery
Open ›The boat's electrical system starts and ends with the battery. It is important to check that the battery is fully charged and in good health before starting to diagnose any electrical problems.
The fuse supplying power to the ignition key is blown
Open ›When you turn the ignition key, a small amount of electrical current is sent to the starter solenoid to activate it. The circuit that supplies power to the key switch is fused, so if that fuse is blown you won't hear the solenoid clicking as it activates.
The gear selector is not in neutral
Open ›Most outboards have a switch inside the selector that stops the starter motor from being activated when the gear selector is not in neutral.
Your starter solenoid is faulty in some way and is not activating
Open ›A failed starter solenoid that no longer activates won't engage the starter and has to be replaced. Links here help you find the correct replacement part number for your motor.
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