What do the candles stand for on the menorah?

In synagogues the Ner Tamid is a continuously burning lamp which hangs over the ark. It is a symbol of the "western lamp" which was the eternal light that constantly burned in the Temple of Jerusalem. Furthermore, it is a symbol of God's unwavering presence and our never-ending faith in God so they never put out the flame. It also symbolizes the guiding light of the Torah and the ever- lasting covenant between God and the Jewish people. They are also intended to draw parallels between God and fire, or light, which is emphasized throughout the book of Exodus in the Torah.
In a Reform synagogue, it is often used to symbolize the light released from the shards of the receptacles that God used to create light and goodness. These lights are never allowed to dim or go out, and in the case of electric problems, different emergency energy sources are often used to prevent it from ending. Though they were once fueled by oil, most today are electric lights. The Ner tamids at Temple Sinai in Worcester, MA, and Temple Israel in Minneapolis, MN, are solar powered, symbolizing that synagogue's commitment to reducing dependencies on non-renewable resources.

The eternal light is the main reason to one of many stories behind the celebration of the Jewish festival of Hanukkah. When the ancient Maccabees rebelled and reclaimed the Temple of Jerusalem, they relit the eternal light. However, there was only oil sufficient to keep the flame burning for one day, and it took eight days to bring new oil. Miraculously, the flame continued to burn until the new oil arrived.

It is often associated with the menorah, the seven-branched lampstand which stood in front of the Temple of Jerusalem. The Menorah is one of the oldest symbols of the Jewish faith. It menorah in the First and Second Temples had seven branches. After the Temples were destroyed, a tradition developed not to duplicate anything from the Temple and therefore menorah's no longer had seven branches. The use of six-branched menorahs became popular, but, in modern times, some rabbis have gone back to the seven-branched menorahs, arguing that they are not the same as those used in the Temple because today's are electrified. The nine-branched menorah used on Chanukah is commonly patterned after this menorah, because Chanukah commemorates the miracle that a day's worth of oil for this menorah lasted eight days.