Strictly translated, a menorah is actually just any sort of candelabra. The one with 9 candles, one set apart from the others is a Hanukah. However, common usage is that the menorah is a candelabra with 8 candles in a row(more or less) and one candle set apart. The candle set apart is called a shamash, and it is used to light all the other candles. The tradition is that you light one candle(not including the shamash) on the first night of Hanukah, two candles on the second night, and so on up to the third night. You light the candles from right to left with the shamash, and say this Hebrew prayer:

Baruch Atah Adonai, Eloheinu Melech Ha'olam, asher kidishanu b'mitzotav, vitzeanu l'hadlich ne'er shel Hanukah.

Which roughly translates to "Blessed are you, Lord our God, Ruler of the Universe, who hallows us with mitzvot, and commands us to light the Hanukah lights." Mitzvot is a hard word to translate, but it roughly means good deeds and commandments. Ask your local rabbi for a better, more detailed explanation.

The point of the menorah is to celebrate the miracle of Hanukah, where God kept the light burning for 8 days in the temple even though there was only oil for one.