The ignition coil is the component that increases battery voltage and sends a surge to the spark plug which ignites the fuel-air mixture. Older engines have a single ignition coil that covers all cylinders, Others, have one coil for each cylinder head (V6 or V8 engines), or one coil for each cylinder in the engine.
The most common problem with the ignition coil is the boot on the coil could be damaged or the coil could crack. If the ignition coils damaged, then the vehicle would not start.
Some manufacturer factory warranties and extended auto warranties cover the cost of an ignition coil replacement. To check if the ignition coil refer to the warranty booklet of your factory warranty, or the service contract of your extended auto warranty.