Oil -- typically olive oil -- symbolizes the good that comes from celestial love. Celestial love is love of the Lord, the highest and purest love we can have. The good of celestial love is the desire to be good springing from celestial love: Wanting to do the Lord's will because you love Him. That's not a state many reach, even in heaven, but it's a beautiful goal. This representation makes sense based on the idea that the sun -- the source of all natural light and heat, and thus all natural life -- represents the Lord, the source of all spiritual light, heat and life. Burning oil was the most pure fire available in Biblical times, thus the closest representation of the sun people could create.

3643. I have noticed that those in heaven dwell beneath a clear, bright sky like that of morning and midday, extending also towards evening, and likewise in a warmth like that of spring, summer, and autumn. But those in hell dwell under a dim, cloudy, and darkened sky, and also in the cold [of winter]. I have noticed that between the two in general a balance is kept; also that insofar as love, charity, and consequently faith are present in angels, they dwell under a clear sky and in the warmth of spring, and that insofar as hatred and consequently falsity are present in those in hell they dwell in thick darkness and in coldness. And as stated above, the light in the next life holds intelligence within it, the warmth love within it, while thick darkness holds insanity within it, and cold hatred within it.