To quit means to stop doing something. You might quit a lousy job or quit eating dessert.
The verb quit can also mean to leave a place or depart from a location. This meaning isn't used as frequently in conversation now as it used to be, but you can still use it to mean leaving somewhere. For example, if you choose to move from sunny California to Maine because you think you'll like the seasons better, you could say you plan to quit California for a colder climate.