The original Menorah was the golden candelabra that God commanded the Jewish People to make and place in the Holy Temple. It had six branches and a stem, making seven lamps in all. The kohanim (priests) lit it once a day. The Torah relates its measurements and design in Exodus 25:31-40.
The Sages teach that the Menorah was the vessel that God used to blend the spiritual light of the World to Come with the physical light of this world. For this reason, the windows in the Temple were narrow on the inside and wide on the outside - to spread out this blended light to the world.
There is a prohibition against making a metal seven-branched menorah. This prohibition is part of the general prohibition against making vessels like those of the Holy Temple, and it was never rescinded.
Chanukah was instituted as an annual holiday the very first year after the Maccabean victory (165 BCE) to celebrate the victory and the miracle of the oil that burned for eight days.
The Chanukah menorah has place for eight candles and for a ninth candle set off somewhat from the rest. The eight candles commemorate the miracle of the oil while the ninth candle, the shamash, is for light. The first use of an eight-armed menorah for Chanukah is not known, although there are some dating back over 500 years.
There's no absolute requirement to use a Chanukah menorah, because you can fulfill the minimal requirement with one candle per night. But since it's ideal to add a candle each night, the custom arose to use an eight-branched menorah. A friend of mine from Yeshiva used to line up eight soda cans as his menorah!
And Feldi, let me know what grade I get, er, I mean, what grade you get, on the report!
Sources:
- Tractate Shabbat 21b
- Tractate Avoda Zara 43a
- Shulchan Aruch Yoreh Deah 141:2
- See also Iggrot Moshe Yoreh Deah 3:33