Oil in the Bible represents the Lord’s love, so anointing someone (or something) with oil was a way to make that person (or object) a representative of the Lord. At the ultimate level, of course, the Lord Himself, as Jesus, is known as “the Anointed,” used with a similar meaning to “Messiah” or “Christ.” Being the Anointed means that he is love itself, presented to us through divinely true ideas. The fact that kings and priests were anointed meant that they also could represent true ideas coming from good loves, on a lower level.

(References: Apocalypse Revealed 779 [2]; Arcana Coelestia 9954; The Apocalypse Explained 375 [7-25], 684 [2-33])