Static electricity and current electricity depend on the accumulation or movement of electrons within an object.
Conductors are materials (typically metals) which have mobile electrons.
In these materials electrons are free to move within the material.
In metals electrons form a "cloud of free electrons" on the surface of the material.
The movement of these electrons accounts for the charge on the material.
In materials called Insulators electrons are held tightly in place and are not allowed to move.
These materials do not easily conduct electricity
-- for example: air, vacuum, glass.