An ignition module is a device in your car's ignition system that triggers the ignition coil, creating the spark that transfers to the spark plugs via the spark plug wire. Ignition modules lead a hard life and must survive millions of high-voltage shocks before giving out. Module problems are frustrating and confusing for those not acquainted with their telltale symptoms.
High RPM Failure
Generally speaking, the first indication of module failure is a stutter at high RPM that feels remarkably like the engine's rev limiter. As the module continues to worsen, the engine's upper-RPM limit will get lower, and the cut will get choppier. Eventually, the condition will manifest itself as high RPM misfire, which can't be mistaken for anything else.
Perhaps the most telling symptom of ignition module failure is temperature-related stalling. Temperature failures most often happen when the module has an internal short or one of its relays stick closed. As current flows through the module, its circuits will overload and refuse to function until they're left to cool. Most often, the car will start and run fine, but will stop running anywhere from seconds to minutes later. The engine may not restart immediately but will do if left to cool for about 10 minutes.
One old-school mechanic's trick is to douse the overheated module with water, which cools it almost instantly. Throwing water on hot electrical components isn't the brightest idea, but it usually works. Generally speaking, any shock to an overheating module will affect how it works, so rapping it with a screwdriver handle can either cause the engine to stall or help it run if it does stall. This kind of shock-test is pretty telling since a properly functioning module won't react at all.
At some point, you'll start to notice hesitation/misfire under acceleration. Consider this symptom separate from high-RPM misfire since it occurs no matter what the RPM and gets worse with throttle application. The vehicle may accelerate under normal conditions without too much drama, but will start to buck and surge when you really lay on the gas. This condition isn't definitive; a lot of things can cause heavy-throttle misfire so don't replace the module unless you've confirmed its malfunction in some other way.
No Start Condition
Eventually, a bad module will result in a failure to start under any condition. Module-related no starts can either be of the "trying to start" or "dry start" variety, depending on how shot the module is. Once you've reached the point of going nowhere, it's time to replace the module.