A pure substance is made up solely of that substance and can't be separated into any other substances. A mixture can be separated into two or more pure substances. While pure substances have clearly defined physical and chemical properties, mixtures have different properties, depending on the proportions of the pure substances in each mixture and on the location in the mixture.
Pure substances can be elements made up exclusively of one kind of atom, or they can be compounds made up of molecules that include two or more elements. Mixtures can be homogeneous or heterogeneous depending on how finely mixed the components are. Homogeneous mixtures have the same look and characteristics throughout the mixture. Heterogeneous mixtures are more coarse with detectable variations in appearance and properties in different parts of the mixture
TL;DR (Too Long; Didn't Read)
Pure substances are made up of one kind of material with consistent properties, while mixtures consist of two or more pure substances, each having different properties. As a result, pure substances can't be separated into other materials, but the different properties of the components of mixtures can be used to separate them into pure substances.
Elements and Compounds
Elements are always pure substances, while compounds are chemical combinations of two or more elements and can also be pure. In the real world, substances such as elements and compounds are rarely pure because they are usually contaminated by their containers, their surroundings or their production. In theory, pure means without detectable impurities,. It is usually possible to purify elements and compounds to that standard, although it often takes a great deal of effort.
Compounds are made up of more than one pure substance, and they differ from mixtures in that it is impossible to separate them without a chemical reaction. Mixtures can be separated by physical processes, but these will not separate compounds.
If an element or compound exists in two states simultaneously, it can be a pure substance and a mixture at the same time. For example, pure water with pure crushed ice in it is still a pure substance, but it is also a mixture of two states of the pure substance. As a mixture, the ice can be separated from the water with physical means such as scooping out the ice fragments.
Homogeneous and Heterogeneous Mixtures
Mixtures contain more than one type of atom or molecule and can be separated by using physical methods. In homogeneous mixtures, the mixture particles are so fine that the mixture looks like it is made up of the same material throughout. For heterogeneous mixtures, the particles are detectable, and the properties of the mixture differ depending on what part of the mixture is examined.
Solutions are typical homogeneous mixtures. For example, a solution of salt in water is a homogeneous mixture because the water and salt can be separated by distillation, producing pure water and crystalline salt. Air is a mixture made up mainly of nitrogen and oxygen. The gases can be separated by cooling and liquefying the air and then boiling off nitrogen, which has a lower boiling point, and then oxygen, which boils at a higher temperature than nitrogen.
Heterogeneous mixtures can be anything from breakfast cereal, to sand or salad dressing. Many common materials are heterogeneous mixtures that can often be separated easily by filtering, mechanical picking apart, or by using properties such as weight or magnetism. The key characteristic of heterogeneous mixtures is that their properties vary from point to point, and that variation can be used to separate them.
For any unknown substance, close inspection usually discloses whether the material is a heterogeneous mixture. If it is not, it could be a homogeneous mixture or a pure substance. Heating or cooling will result in the material either separating out as the mixture components boil or solidify at different temperatures, or the whole pure substance will boil or freeze at single points.