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.

6315. The person whose life has been raised up from the level of the senses by means of the good of faith is by turns in light on the sensory level and in light on a more internal one. When worldly cares occupy his attention, or he is among groups of people in which external interests flourish, or he indulges in mere pleasures, he is living on the sensory level. In this state he avoids and also objects to talking and thinking about God and matters of faith. If he did talk or think about them in that state he would consider them to be worthless unless he were instantly raised by the Lord from that level to more internal things. But when that person is not taken up with worldly things but sees in light on a more internal level, what is right and fair is the basis of his thought; and if he sees in light on a still more internal level, what is spiritually true and good is the basis of it. The person who leads a good life is raised from light on one level to that on another; he is raised to a more internal level the instant he begins to have evil thoughts, for angels are close by him. I have been allowed to know these things through experiences I have had, for I have frequently been aware of being raised up, and at the same time of changes of state in both my affections and my thoughts.