Anointing oil (in Hebrew
שמן המשחה Shemen haMishkhah, oil of anointing) was an important part of the ordination of priests and kings in biblical times and the Temples in Jerusalem. It sanctified those who were anointed with it and set them apart as holy, and devoted them to God. One of the articles of the Tabernacle, it was originally only used in the Temple, afterwards being used to anoint kings as well (I Samuel 10:1), and was forbidden to Jews for use outside of these designated purposes on any common person or to duplicate it.
Nowadays however, and in Christianity, anointing oil is used in devotional practices, in various liturgies, and is not forbidden. In fact, its use is encouraged for devoting oneself, others, or objects to

the service of God.
The word Messiah derives from the word mishkhah, meaning anointing, because the Messiah was anointed in
anointing oil when recognized as such, and indeed, Jesus was anointed as a king a priest and a prophet, all of the things which are anointed positions.
"Is any among you afflicted? let him pray. Is any merry? let him sing psalms. Is any sick among you? let him call for the elders of the church; and let them pray over him, anointing him with oil in the name of the Lord." (James 5:13,14 (KJV))
Christianity uses anointing oil for curing the sick, praying, and devoting things to the worship of God.
There are many variations of anointing oil used now, as the precise recipe of the original has been lost, but they all include olive oil and other essential oils from the region. Using an anointing oil made in the holy land out of Israeli ingredients is as close as you can get to the anointing oil of biblical times. They can smell quite lovely and function as a wonderful way to devote yourself fully to your prayers or devotions, and remind you of your connection with God and Jesus.
Jews in this day and age typically do not use anointing oils.