The vapor pressure of a pure component is the pressure exerted by the vapor on the liquid in a closed system.
A liquid boils when the vapor pressure of the liquid is equal to the atmospheric pressure.
A miscible solution boils at a temperature between the boiling points of the pure components. The vapor pressure of the mixture is equal to the sum of the product of the partial vapor pressures and mole fractions of the components.
Initially, the vapor — and by extension, the distillate — is rich with the more volatile component. As that component boils off, the less volatile component enters the vapor phase. At the end of the distillation, the vapor phase is rich with the molecules of the less volatile component.
The vapor-liquid diagram is a plot relating the temperature of the vapor and liquid to the mole fraction of each component. At a given temperature, the composition of the liquid and vapor phases can be determined.