Answer:
Halachicly (by Jewish law) it means that your mother is a descendant of Abraham or that she was converted to Judaism.
But you are only really behaving Jewish when you accept this and live by the Jewish laws.
Reform and Reconstructionist Judaism also recognize someone as Jewish if they have a Jewish father AND they are raised Jewish. There is debate within the Conservative movement to add this definition as well, since Judaism was patrilineal in the Torah, but at the moment, this view doesn't have any support.