This is completely unrelated to what "self-rule" means at other levels and in ordinary speech. Why the special definition for cities?
This is the concept at play at the municipality level that is being discussed. The cities run themselves unless the state has to step in for some reason. Just as the states run themselves unless the federal government needs to step in for some reason.
This is as opposed to say, a village, which in New England at least is defined as a population center which is not self-governed, but under the direct control of a larger municipality within which it lies.
Jews in medieval Europe were generally subject to Jewish law and not subject to the law that applied to the rest of the city. That's self-rule.