Azeotropes exist as an explanation (or terminology) for non-ideal mixtures. Remember that Raoult's law says that each component of a mixture produces it's own specific effects on that mixture, and that all of these effects can be summed together (ex. vapor pressure of the total mixture). However, azeotropes take into consideration what happens when this is not the case - when the mixture is not ideal. For instance, after myriad distillations you may be left with a product that is not entirely pure but that can not be made any "more pure" by continual distillation because the product acts as a pure liquid - this is an azeotrope.