Heat moves between objects by conduction (touching), by convection (circulating) and radiation (sending heat rays). An insulator is something that stops the heat from being passed from one object to another.
Normally we look for a material which can do more than one of these jobs. For example we can stop heat rays reaching something by reflecting it back using aluminium foil. That is why many insulation materials have a shiny surface film.
We can stop heat being transferred by convection if we can keep the air still. The best way to do this is to trap the air in a mesh of fibres. That is what fibreglass insulating material does.
Air itself is a very good insulator that stops heat being transferred by touch. You know this because when you touch insulating material it feels warm (that is we are not giving up heat when we touch it).
So a fibreglass insulating material is made of an insulator glass, spun into a web that traps the insulator air, and often has a surface coating of aluminium foil as well.