fine flour: the finely milled, sifted top grade of wheat flour
Fine flour is the best, most carefully refined wheat flour, smooth and pale, with the bran and coarse grit sifted out. It is the premium product, a step above the everyday ground meal an ordinary household used, and the Bible treats it as something fit for honored guests, a king's table, and above all for God.
The word names one substance, but it shows up in two very different settings, and that is the whole interest of it. By far the most common use is in worship: fine flour is the standard material of the grain offering, measured out, mixed with oil, and brought to the altar all through Leviticus and Numbers. The rest of the time it is simply the choicest flour on hand, the kind Abraham hurries to bake into bread for his three visitors, the kind stocked daily in Solomon's kitchens, sold in the market, or listed among the luxuries God lavished on Jerusalem.
The link between the two settings is the idea of giving God the best. Israel did not offer coarse, second-rate meal; the grain offering called for the same fine flour a person would set before an important guest, which is part of what made it an offering and not just a donation of food.