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.

135. And thou holdest My name, signifies the acknowledgment of the Divine in the Human of the Lord, as well as all things of love to Him and faith in Him. This is evident from what has been shown above about the signification of the "name" of Jehovah, Lord, and Jesus Christ n. 102. By the Lord's "name" in the Word is meant primarily the acknowledgment of the Divine in His Human, because all things of love and faith are from that; for Divine goods which are of love, and Divine truths which are of faith, proceed from no other source than from the Lord alone; and these cannot flow in with man unless he thinks of the Lord's Divine at the same time that he thinks of His Human; nor is His Divine separate from the Human, but it is in the Human (as may be seen above, n. 10, 26, 49, 52, 77, 97, 113, 114). I can aver, from all experience of the spiritual world, that no one is in the truths of faith and in the goods of love except he who thinks of the Lord's Divine at the same time that he thinks of His Human; as also that no one is spiritual, or is an angel, unless he has been in that thought and consequent acknowledgment in the world. Man must needs be conjoined to the Divine by his faith and love in order to be saved; and all conjunction is with the Lord; and to be conjoined to His Human only, and not to His Divine at the same time, is not conjunction; for the Divine saves, but not the Human apart from the Divine. (That the Human of the Lord is Divine, see The Doctrine of the New Jerusalem 280-310.)