A Chanukah menorah must contain enough fuel at the time of lighting to burn for at least half an hour after nightfall. Based on this, Rabbi Tzvi Pesach Frank, zatzal, head of the Rabbinical court in Jerusalem, ruled that one may not use an electric menorah. Electricity is not stored for future use; rather, it is consumed as it is generated. Thus the required amount of "fuel" is not in existence at the time of lighting. (According to this, a battery-operated menorah should be OK, because the fuel actually is there at the time of lighting.)
Another reason not to use an electric menorah is that the menorah we use commemorates the Menorah in the Temple and the miracle that occurred there. Our menorah, therefore, should resemble the one in the Temple. For that reason, many people use olive oil for fuel. Someone even markets candles made of congealed olive oil for use as Chanukah and Friday night candles!
