The oil of olives was widely known and used during most of Bible History. It had a wide variety of applications, and was a valuable commodity. It was used for anointing the living and the dead, for sacred offerings, for lighting lamps (in the Tabernacle, Temple or in ordinary people's homes), cooking and medicinally. It was also used in personal grooming, and as an ingredient in some soaps (as it still is). Depending upon circumstances, the oil was produced by various methods, from beating or trodden, or in a press or mill powered by humans or oxen. Olive oil was also used figuratively for the Holy Spirit.
"Oil in the name of The Lord"
Olive oil was used to light the golden lamps in both The Tabernacle In The Wilderness and The Temple In Jerusalem (see The Menorah):
"And you shall make a lampstand of pure gold. The base and the shaft of the lampstand shall be made of hammered work; its cups, its capitals, and its flowers shall be of one piece with it; and there shall be six branches going out of its sides, three branches of the lampstand out of one side of it and three branches of the lampstand out of the other side of it; three cups made like almonds, each with capital and flower, on one branch, and three cups made like almonds, each with capital and flower, on the other branch - so for the six branches going out of the lampstand; and on the lampstand itself four cups made like almonds, with their capitals and flowers, and a capital of one piece with it under each pair of the six branches going out from the lampstand. Their capitals and their branches shall be of one piece with it, the whole of it one piece of hammered work of pure gold. And you shall make the seven lamps for it; and the lamps shall be set up so as to give light upon the space in front of it." (Exodus 25:31-37 RSV)
"So Solomon made all the vessels that were in the house of The Lord: the golden altar, the golden table for the bread of the Presence, the lampstands of pure gold, five on the south side and five on the north, before the inner sanctuary; the flowers, the lamps, and the tongs, of gold; the cups, snuffers, basins, dishes for incense, and firepans, of pure gold; and the sockets of gold, for the doors of the innermost part of the house, the most holy place, and for the doors of the nave of the Temple" (1 Kings 7:48-50 RSV)
Priests and kings were anointed with olive oil, perhaps partly as an analogy of the oil providing light, as in enlightenment.
"And he [i.e. Moses] poured some of the anointing oil on Aaron's head, and anointed him, to consecrate him." (Leviticus 8:12 RSV)
"Then Samuel took the horn of oil, and anointed him in the midst of his brothers; and the Spirit of The Lord came mightily upon David from that day forward" (1 Samuel 16:13 RSV)
"There Zadok the priest took the horn of oil from the tent, and anointed Solomon. Then they blew the trumpet; and all the people said, "Long live King Solomon!" (1 Kings 1:39 RSV)
Olive oil was extensively used in various offerings:
"Now this is what you shall offer upon the altar: two lambs a year old day by day continually. One lamb you shall offer in the morning, and the other lamb you shall offer in the evening; and with the first lamb a tenth measure of fine flour mingled with a fourth of a hin of beaten oil, and a fourth of a hin of wine for a libation" (Exodus 29:38-40 RSV)
"And this is the law of the sacrifice of peace offerings which one may offer to The Lord. If he offers it for a thanksgiving, then he shall offer with the thank offering unleavened cakes mixed with oil, unleavened wafers spread with oil, and cakes of fine flour well mixed with oil." (Leviticus 7:11-12 RSV)
Olive oil was used for medicinal purposes:
"From the sole of the foot even to the head, there is no soundness in it, but bruises and sores and bleeding wounds; they are not pressed out, or bound up, or softened with oil." (Isaiah 1:6 RSV)
"But a Samaritan, as he journeyed, came to where he was; and when he saw him, he had compassion, and went to him and bound up his wounds, pouring on oil and wine; then he set him on his own beast and brought him to an inn, and took care of him." (Luke 10:33-34 RSV)
"Is any among you sick? 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; and the prayer of faith will save the sick man, and The Lord will raise him up; and if he has committed sins, he will be forgiven." (James 5:14-15 RSV)
Olive oil was used for the dead and the dying, including for Jesus Christ:
"In pouring this ointment on My body she has done it to prepare Me for burial. Truly, I say to you, wherever this Gospel is preached in the whole world, what she has done will be told in memory of her." (Matthew 26:12-13 RSV)
"This man went to Pilate and asked for the body of Jesus. Then he took it down and wrapped it in a linen shroud, and laid Him in a rock-hewn tomb, where no one had ever yet been laid. It was the day of Preparation, and the Sabbath was beginning. The women who had come with Him from Galilee followed, and saw the tomb, and how His body was laid; then they returned, and prepared spices and ointments. On the Sabbath they rested according to the Commandment." (Luke 23:52-56 RSV)
Fact Finder: How was olive oil used in the parable of the "Ten Maidens"?
See How Much Oil Is In Your Lamp?