The hanukkiah is a nine-branched lamp lit over the eight nights of Hanukkah, and it is defined by a distinction that is easy to miss: one of its nine lights is not counted at all.
Eight, and the servant
Eight lights stand for the eight nights, one added each evening until all eight burn on the last night, recalling the tradition that a single day supply of oil in the rededicated Temple burned for eight. The ninth light, set apart in height or position, is the shamash, the servant, used to kindle the others because the Hanukkah lights themselves may not be used for any practical purpose, only looked at. The whole arrangement is built to keep the eight commemorative lights pure of ordinary use, which is why a lamp for kindling them must be added.
Publicising the miracle
The hanukkiah is placed where it can be seen from the street, in a window or a doorway, because the point of the observance is the publicising of the miracle, the public proclamation of the deliverance it recalls. This is why it has served, like the shofar, as a barometer of Jewish security, since a lamp displayed in a window is only displayed where Jews feel safe to be seen. It is regularly and mistakenly called a menorah, but the seven-branched menorah is a different object of the Temple, and the nine-branched Hanukkah lamp is its distinct and later relative.