Why is my laptop making a clicking noise?

Check if an external device is connected and potentially causing the noise: If there is any external device, such as a USB drive, connected to the computer, unplug it and see if the noise continues.
Inspect the laptop fan:
Look at the fan on the side or the bottom of the laptop and inspect if there is any debris preventing the fan from spinning freely. If there is a blockage, use some compressed air to remove it.
Check if the CPU is overheating:
Use a temperature monitor to see if the temperature of the CPU is too high. If it is, clean off the dust and any other debris on the vents.
System Restore:
If nothing seems to work, try restoring the computer back to the OEM configuration.