A conductor is a material which enables electrons to flow freely between atoms.
Most metals are regarded as conductors which have valence electrons in the outer shell that are free which repel each other. Once an electric field is applied to copper the free electrons propagate through the medium.
Different materials exhibit different levels of conductivity. Silver is a better conductor than copper for example as it has a valence electron in the fifth shell which is even further way from the nucleus which means it requires less energy to conduct than copper which has a valence electron in the fourth shell. A silver atom diagram is shown below:
An insulator is a material which strongly resists the flow of electricity. As opposed to conductors, the outer electrons are tightly bound so that there is almost no flow even with an electric field present.
Most solid materials are insulators. Argon is an example of an insulator and we can see from the diagram below the tight grouping of the electrons in the outer layer.
Note however that insulators can become conductive if a large enough voltage (energy per coulomb of charge, which we will learn about in the next topic) is applied to take the electrons away from the atoms and is known as the breakdown voltage.