My "Check Engine" warning light stays on while driving. What does this mean? Could it mean serious trouble?

It means that one of the engine sensors is going. such as an O2 sensor

Appreciate your response, thank you.

michgt also be the sensor on your cad, check that first, u got 2 sensorsors on the mufflers and 1 on your cad , its not serious

It could mean hundreds of different things some of which could be serious. Read the trouble codes to find out where the problem is. Some parts stores will do this for free or you can purchase your own scan tool.

Take your car to Autozone. They'll pull the codes from your car's computer and they can tell you if you have a cylinder missing, a cat going out, or any other thing the computer is reading; then they can give you a list of steps to take to troubleshoot that problem.