Materials are divided into three categories, depending on how easily they allow charge (usually electrons) to flow along them. These are:
In conductors the outermost electrons in the atoms are so loosely bound to their atoms that they're free to travel around the metal. In insulators the electrons are much more tightly bound to the atoms, and are not free to flow.
Charge flows far more easily through conductors than insulators, which is why wires you plug into a wall socket are covered with an insulating coating. Charge flows along the wire, not through the coating to you.
Semi-conductors are a useful intermediate class, not as conductive as metals but considerably more conductive than insulators. By adding impurities to semi-conductors in appropriate concentrations the conductivity can be well-controlled. This is exploited in integrated circuits you find in cell phones, computers, etc.
In the animation a positively charged insulating rod is brought close to an electroscope - note how the charges on the rod stay fixed in place.
Because the electroscope is made from conducting material, some of its electrons move up to the top of the electroscope to be near the charged rod when the rod is held close. The electroscope has a net charge of zero at all times here, but the rotating arm seems to indicate a net charge because of the way the charge on the electroscope is shifted. This is how an electroscope can be used to indicate the presence of a nearby charge.