Won't crank, or do you mean won't start? They're different.
When talking with your mechanic, (hereafter referred to as your "tech"), you don't need to know "mechanic speak," but it helps to know some common technical terms, and what they mean to him or her, (hereafter referred to as "Him"). These terms often mean something different to different people, resulting in that great line from the movie "Cool Hand Luke" - "What we have here is a failure to communicate," and they were not even trying to fix a car. They had is easy in that prison.
For instance, say your car won't start one morning. You call your tech, and he asks if it will crank. You reply no, that's why you called him. You already said it won't start. Hold on. Here's the problem. To a tech, cranking is what happens when the starter spins the motor, whether it starts up or not. Think about the old Ford model "T" cars, where the driver stuck a crank handle through the front grill, into the engine, and cranked the handle to turn the engine over until it started. That was cranking. That job is now done with an electric starter motor, but it is the same operation.
The engine can crank without starting. So, the question the tech is asking is leading him down a diagnostic trail. Cranking involves a battery and a series of switches, relays, solenoids and a starter motor. If it cranks, but doesn't start, he knows this whole system is good because it's doing its job. The problem therefore could be the auto is out of gas, has a bad fuel pump, or has a failed ignition system. If, however, it won't crank, it means a possible dead battery or a problem in that string of switches and relays, and we won't worry about the fuel or ignition systems, because they have nothing to do with cranking.
About that "dead battery" thing; when a battery dies, something killed it. Like with a murder mystery, it could have been old age, or it could have been caused. If you don't get to the bottom of this, and simply replace the battery, that same cause can kill the new one also. Now you're out the cost of the replacement battery, you disposed of a good one, and still have to repair the problem. Always get a solution to the mystery of the dead battery before replacement. It might be a short in the car, or it might be the butler. It is a mystery, after all. Let's remove some of the mystery.
Here's how a battery works in your car. Think of it as a very strong wind-up spring. It has only two jobs to do: crank your engine until it starts, or play your radio while you sit with the engine off. Both of these jobs cause the spring to unwind a bit. When the engine starts, the alternator winds up the spring again and provides all the electrical power needed by the car. The battery does nothing at all until you turn the engine off, then it's ready to crank again when needed. If you leave the lights or radio on too long with the engine off, the spring will unwind so far that it cannot crank the car. It's not the battery's fault. It's yours, in this case. It can be wound up again (charged), and you're good to go. With age, some batteries fail, like a broken spring would do. Don't think you will get a warning that it's about to happen. You usually don't. A broken battery is easy to diagnose with the proper equipment, so there's no reason to guess about it. Many good batteries are wasted this way.
By the way, battery manufacturers tell us that the average life of a battery in Florida is less than three years. Some have gone 10 or more, some fail at one or two years. Bigger engines require bigger batteries. All car batteries are 12 volts, but there are dozens of different sizes and shapes made to fit different cars, and they do not easily interchange. Car manufacturers do not make batteries. Battery manufacturers do, and they make various qualities of batteries. Better batteries last longer, are heavier, and cost more than inferior batteries.
You really do get what you pay for with batteries, and you can't do without them. Cars don't come with crank handles anymore. Be glad about that.