Your car shut off while driving and never started back up what could be the problem?

I can guarantee that it's electrical or mechanical.

Sorry to sound flippant, but the reality is, there are quite a few problems that can cause what you describe; without additional information there is just no way to know for certain.

To help isolate the problem:

try using a little starting fluid, see if you can start the engine briefly with that. If the engine isn't getting fuel the starting fluid will let it run briefly, and it will verify that everything else is working properly. Once you do that you have eliminated a whole list of other potential problems.

If the starting fluid is used properly and the engine doesn't start, check for spark. Pull a plug wire and connect it to a spare sparkplug. (hint: it doesn't even need to be a sparkplug that fits your car) Have a friend try to start the car and watch the sparkplug to verify that you're getting a good, strong spark. If not, you can go from there.

If you have spark AND starting fluid didn't tell you anything, run a compression test. Poor compression indicates something SERIOUS inside the engine.

The point is, you need to isolate the problem.

Simply making the statement: "My car won't start. What's wrong?" will not result in many people wanting to give you any help.