wood, crystal, diamond, stone, granite
This is sort of a complex answer, so I'll separate it into parts that at least make sense to me.
The first answer is that given enough potential, anything will conduct electricity. There is a method of radioactive waste neutralization called volcanization that takes this principle to heart, in essence you put a piece of radioactive waste in the ground between two strong electrodes and jam so much potential that it literally glasses the ground and the waste.
The second answer applies to room temperature and common, mostly dry situations; only metals will conduct electricity. Dry salts and covalently bonded molecules, or other non-polar molecules will not conduct electricity. This has to do with metals electrical structure, they have this 'sea' of electrons that flow easily between metal atoms, whereas in ionic molecules electrons are stolen outright and the cyrstals are held together through electrostatic force, and in covalently bonded molecules the electrons are held in tight bonds between two atoms.
The third answer applies to when things are wet; metals still conduct, that's almost always a given, but when aqueous(dissolved) salts will make ions, which are charged particles, and will conduct. This is why pure deionized water is non-conductive, but tap water is. Its because tap water has many different salts and charged species capable of conducting in it. Polar molecules will also conduct electricity, albeit weakly.
TL;DR Metals always conduct, water will conduct when a salt is dissolved in it.
This is the definition of an "insulator". Materials that block or impede the flow of electrons will prevent electric current from completing a circuit.
rubber would be an example of something that does not allow electricity to move through it easily
The path of electricity is called a circuit.
Things that electricity move through easily are called conductors. The reason electricity moves through these materials more easily than others is that the electrons in these materials are not tightly bound or even associated with any particular atom. Physicist like to think of the the electrons in conductors as forming some kind of charged gas or liquid. They call it a sea of electrons. Please take note that I do not mean to send the impression that electrons in a conductor LITERALLY form a liquid or gas, but their movements are such to lend themselves to that analogy. We think of a wire kind of as a water pipe. One droplet of water entering the pipe on one side sends precisely one drop of water out of the other side. Really electricity is motion, the motion of charge carrier (electrons in metals). Their movement is a response to the electric field, which is a consequence (in a circuit) of a non-uniform distribution of charges.
That would be an impermiable materials.
As unsatisfying as I'm sure you'll find this, that depends on your definition of "electricity." If you mean electricity in the most conventional sense of an electrical current, electricity can move through any medium in which charge carrying quantons (protons, elecrtons, etc) can move at least somewhat freely.
rubber would be an example of something that does not allow electricity to move through it easily
Electricity can move through materials that conduct electricity well, such as metals like copper and aluminum. It can also move through materials that allow some level of conductivity, like water and the human body. Insulating materials, such as rubber and plastic, prevent the flow of electricity.
insulators
conductors
rubber would be an example of something that does not allow electricity to move through it easily
Rubber is what is known as an electrical insulator. The difference between insulators, which block the flow of electricity, and conductors, which permit the flow of electricity, lies in the availability of mobile electrons in the material in question. Electricity is composed of moving electrons. Some materials, such as metals, contain electrons that are easily moved, hence electric currents move easily in those materials. If a material does not have electrons that are easily moved, then it resists the flow of electrons.
One example of a material that does not conduct electricity or heat effectively is a type of plastic called teflon. Teflon is non-conductive and has a low thermal conductivity, making it useful for insulating electrical wires and preventing heat transfer.
Electricity moves through materials when there is a flow of charged particles, typically electrons, along a pathway provided by the material's structure. Conductive materials such as metals have free electrons that can move easily through the material, allowing electricity to flow. Insulating materials, on the other hand, impede the flow of electrons, preventing electricity from moving through them.
Materials that are good conductors of heat, like metals such as copper and aluminum, allow heat to flow easily through them. These materials have high thermal conductivity, enabling heat to be transferred quickly from one place to another. On the other hand, materials with low thermal conductivity, such as wood or plastic, inhibit the flow of heat.
Materials that allow electrons to move through them easily are called conductors. Common examples of conductors include metals like copper, silver, and gold. The presence of free electrons in the material facilitates the easy flow of electrical current.
The path of electricity is called a circuit.
An insulator is a material in which charges cannot easily move due to the lack of free electrons. Examples of insulators include rubber, glass, and plastic. Insulators are used to prevent electric current from flowing through them, making them good materials for electrical insulation.