A tech came out to the house to check on the central air unit. The downstairs heater is not working. Apparently he told my wife that he had to jumpstart the motor for it to turn on. Does this mean a capacitor is bad or the motor is bad?
Thanks

If the motor sits there humming and getting hot it doesn't have starting torque.
That's what the capacitor provides (along with running torque).
The only thing I can gleen from the term jumpstart is the "tech" spun the fan blade to get the motor running and should have sold you a capacitor. If the motor amperage is above the rated amps on it's label (with a new capacitor) you probably will need a new motor soon.

Trained and experienced technicians have already made all their mistakes. Home repairs that are outside of your abilities can result in catastrophe's.