An azeotrope (from the Greek a, not + zein, to seethe + tropos, turning change) is a condition of a liquid mixture whose equilibrium vapor has the same composition as the corresponding liquid.

The most common example of an azeotrope is that of ethanol (common alcohol) and water. At 1 atm., this mixture forms an azeotrope at 89.43 mol% ethanol. This means that an 89.43 mol% ethanol solution cannot be further purified by binary distillation, since the vapor that is boiled off contains 89.43% ethanol, and the remaining liquid also contains 89.43% ethanol.

Azeotropes are a drastic restriction on the ability to separate components using distillation for many mixtures. The azeotrope is caused by nonideality of the liquid mixture. This means that there are strong attractive or repulsive forces between the molecules of the different species.

In the case of repulsive forces, the molecules repel each other -- for example "cowboy" molecules and "indian" molecules1 (I won't take blame or credit for this analogy). The indian molecules are the light (more volatile, lower boiling) component. Let's start at the situation where there are only indians. If we throw in a few molecules of cowboys, they try strenuously to escape. Because of this tendency, they will boil off more quickly as compared to a solution made up of cowboys alone. But the indians (the more volatile) are boiling off as well. If we add more cowboys to the system, we will eventually reach the point where the ratio of cowboys-to-indians that is boiled off is equal to that remaining in the liquid. This point is called the azeotrope, or more precise a Minimum-boiling azeotrope.

If the molecules attract, rather than repel, the opposite occurs. This is called a Maximum-boiling azeotrope. In this case the molecules of the two components have a tendency to stick together, resulting in a lowering of the apparent boiling point of the mixture. In fact, mixtures with strong attractive forces can have a boiling point that is higher than the boiling point of the pure heavy component.

1: William L. Luyben, Leonard A. Wenzel, Chemical Process Analysis: Mass and Energy Balances, Prentice Hall, 1988.
Phillip C. Wankat, Equilibrium staged Separations, Prentice Hall, 1988.