For some reason, I began wondering if there were fires around the world that burns continuously.
Only then did I find out about eternal flames. Not the song by The Bangles, but real flames that keeps burning, naturally or deliberately.
What do they signify?
Off the top of my head, I would say that the eternal flames that are deliberately kept burning represent the continual burning of a cause, or a memory. It takes time, care and resources, and it represents the fact that we will never give up on the cause or memory that the fire is burning for.