Many people complain of an engine that clicks when they are trying to start their vehicle.
The most common answer to this problem is usually the battery. Often times a low battery will have enough juice to power the starter, which makes the clicking noise, but not enough to get the engine started. This happens if the lights have been left on or if it is plain old and needs to be replaced.
A second answer is that the battery terminals are corroded and in this case, the battery will also need replacing.
If you find this problem occurring on a regular basis, take your car to a professional. They will be able to see if the battery is storing energy properly and also if the charging system is keeping the battery charged with that energy. If either the battery or charging system is out of commission, your vehicle's starter will continue to click.
The worst case scenario here is that your battery is completely dead and needs replacing or that you have an alternator problem. Your best bet is to get the system checked to see which option is making your car click.