What does the menorah symbolize?

The menorah is a religious symbol in Judaism. The original 7-branch menorah was placed in the Temple and its flames burned at night (Leviticus ch.24). In modern synagogues, a single flame (usually electric) represents this ancient mitzvah.

It symbolizes G-d's eternal presence among the people.

Other information:

The Hanukkah-menorah (also called a Hanukkiyah) is an eight-branched candle holder used on the 8 days of Hanukkah. Eight of the flames symbolize the eight days of the miracle, while a ninth candle is next to them and is used to light the others.