Conductors are the materials that easily allow flow of electric current upon application of voltage, such as copper.
Conductivity is the measure of how easily current will flow through that material and shown by the symbol σ (sigma). Its unit is Siemens / meter (S/m) but usually milliSiemens / meter is used. It is a characteristic property a material. In other words, it is not affected by the geometry or size of material.
Insulators are the materials that do not allow or very hardly allow the flow of electrical current upon application of voltage. Example: Glass.
Resistivity is the exact opposite of conductivity and shown by the symbol ρ (rho). So if we were to write resistivity in terms of conductivity:
ρ = 1/ σ
And its unit is:
Ohm meter (Ω.m)
Like conductivity, resistivity is also a characteristic property of the material.
Do not confuse resistivity with resistance. Unlike resistivity, resistance is not a characteristic property and depends on geometry of the material. We can find the resistance of a material if we know its resistivity and geometry. So two cables of the same material with different geometries will have different resistance. We calculate resistance from resistivity as below:
So this means that as the length of a material increases, the flow of current through it will be more difficult and the resistance will increase. And when its area increases, the resistance will decrease as the current will flow easier.
Semiconductors are the materials that allow flow of current easier than resistors but harder than conductors. Examples: Silicon, Germanium.
In semiconductors, electrons can change their place (thus make current flow possible) only after a certain amount of voltage is applied. By controlling this, we can control when a current will flow or not, depending on our purpose in an electrical circuit. This key principle enables all electrical devices that we use today to function as we want.