"Cure or quit" is a phrase that means you either need to fix something completely or stop doing it altogether. For example, if you have a problem with eating too much candy, you might need to either find a way to stop eating so much candy, or just stop eating candy altogether.
This phrase is often used when people have an addiction, like smoking or drinking. If someone has a problem with smoking cigarettes, they might need to quit smoking altogether. But if they want to keep smoking, they might need to find a way to cure their addiction to smoking, like going to a class or support group that helps people quit smoking.
Basically, "cure or quit" means that if something is hurting you or causing problems in your life, you need to either fix the problem completely or stop doing it altogether.