A fractionating tower works by creating a temperature gradient from the bottom to the top of the column, with the highest temperature at the bottom. The vapors rise up the column until they reach the part of the column that is at their condensation temperature, where they condense to form a liquid. The lower the boiling point of the liquid, the higher up the column they will have to go before the temperature is low enough for them to condense. Oxygen, which has a higher boiling point, will condense lower on the column, while nitrogen, with a lower boiling point, rises higher in the column.
This is a different system from what you typically see in a lab distillation system. In a lab system, you slowly raise the temperature of the pot, and as the boiling point of each component is reached, that component will boil off and the vapors can be collected at the top of the column. With a fractionating tower, the temperature of the pot is high enough to boil all of the components, and the temperature gradient along the tower determines where the vapors of each component will recondense.
This is a very simplified explanation and ignores the entire theoretical plate concept of fractional distillation, but it should at least explain why the lowest boiling materials are removed from the highest parts of the column.