When you distill a mixture, you are seperating components based on their different boiling point. Consider a mixture of 2 miscible liquids A (bp 70C) and B (bp 120C). When you distill the mixture, you will discover that your mixture first boils at 70C, then it boils at 120C. The fact that you observe more than 1 boiling point indicates there is more than 1 type of substance present in the mixture.
However, in reality, the actual recorded boiling point will not be 70C or 120C because more than 1 component is present in the liquid phase. If liquids A and B forms intermolecular bond stronger than the intermolecular bonding among A molecules and among B molecules, then there will be an elevation in the boiling point of the mixture. If the intermolecular bond is weaker, then there will be a drop in the boiling point of the mixture. It all depends on the mole fraction and the strength of intermolecular bonding between components A and B.