What is the Lamp in the synagogue?

Answer 1

I assume you are referring to "The Eternal Flame" that synagogues keep lit 24/7. This Eternal Flame (Hebrew transliteration "Ner Tamid") is a remembrance of the eternal flame that existed in the Temple in Jerusalem (destroyed 70 CE). The flames on the sacrificial alter were kept burning at all times. Similarly, the menorah (7 branched candelabra) was lit in an offset manner, so that five wicks were lit at once while the other two had been lit earlier. When the two went out, the five were still burning and then when the five finished, the two were still going -- in this way, there was always some light from the menorah. The menorah signifies Torah, and in this way, it corresponds to the ever enduring essence of the Torah -- never extinguishing.

Answer 2

it is a Ner Tamid a continuously burning lamp, which hangs above the Ark. Someone has the Job to make sure it never goes out

Answer 3

It's called a Ner Tamid.