The eight candles of the menorah signify the miracle of a single day's worth of olive oil burning for eight days. When the Maccabees retook Jerusalem from the Seleucids, they wanted to rededicate the temple. Unfortunately, there was only a single flask of sacred oil for the temple menorah, and it would take eight days to produce more. They lit the menorah anyway, and the oil burned for eight days.
In ancient Israel, the menorah was a seven-branched lamp that was kept lit day and night inside the temple. It required a special supply of olive oil as fuel, and this oil had to be blessed and sealed by the high priest. The Seleucid Empire attempted to force their own beliefs on the Israelites, and had desecrated the temple and destroyed most of the supply of oil stored there, leaving only the one small flask that provided the miracle.
Modern menorah have a total of nine branches, four on each side and one in the middle. The candle on the central branch is lit first, and it is used to light the others, one for each night of the Chanukah festival. Typically, menorah are displayed prominently near windows in order to remind others of the miracle.