fresh oil: the newly pressed olive oil of the harvest, counted among a land's staple produce with grain and new wine
Fresh oil is the oil that runs from the olive press at harvest, gathered in while it is new. Almost every time the word appears it stands in a fixed trio with new grain and new wine: the three crops that summed up the yield of the land, what a household lived on, what filled the storehouses, and what was owed to God as firstfruits and tithe.
Because it names the produce of a good year, the word tracks the covenant. When God blesses, the grain, new wine, and fresh oil overflow; when he judges, they wither in a drought or are carried off by an enemy. So the word is less about oil as a substance than about oil as a sign of a fruitful land and a people at peace with God.
This one everyday meaning is stretched once, in a vision of the prophet Zechariah, where two leaders are called sons of the fresh oil. There the harvest word is chosen instead of the ordinary word for anointing oil, marking the two men as freshly supplied and set apart for God's work.