A hanukkiyah is a candelabrum with eight candleholders in a row and a ninth candleholder set a little above the others. It's different from a menorah, which has seven branches and was used in the Temple before it was destroyed in 70 CE. A hanukkiyah is nevertheless a kind of menorah.
The hanukkiyah is used during the Jewish holiday of Hanukkah and commemorates the miracle of the oil. According to the Hanukkah story, once Jewish revolutionaries had retaken the Temple from the Syrians they wanted to rededicate it to God and restore its ritual purity. Eight days worth of oil were needed to complete the ritual purification, but they were only able to find one day's worth of oil. They lit the menorah anyway and miraculously the oil lasted for eight full days.
In commemoration of this event Hanukkah is celebrated for eight days and a candle is lit on the hanukkiyah on each of those days. One candle is lit the first night, two the second, and so on, until the final night when all the candles are lit. Each of the eight candles is lit with a “helper” candle known as the shamash. The shamash is lit first, is used to light the other candles, and then is returned to the ninth candle spot, which is set apart from the others.
How to Use a Hanukkah Menorah
It is customary to light the candles from left to right, with the newest candle being in the leftmost spot. This custom arose so that the candle for the first night would not always be lit before the others, which might be taken to symbolize that the first night was more important than the other nights of Hanukkah.
It is also customary to place the lit hanukkiyah in a window so that passersby will see it and be reminded of the miracle of the Hanukkah oil. It is forbidden to use the light of the hanukiyah for any other purpose – for instance, to light the dinner table or to read by.