As stated in Bob D's answer, batteries do not supply electrons to a conductor. The electrons are already present in the conductor, bound by weak electrostatic forces to the nuclei of the atoms of the conductor, so they are not entirely "free".
When a battery is connected to the ends of a conductor, it exerts a force on the electrons in the conductor (we usually say it generates a potential difference between the ends of the conductor which means the same thing as exerting a force on the electrons) and the electrons move readily since they were previously weakly bound.
An insulator also contains electrons but the electrons are bound to the nuclei of the insulator by very strong electrostatic forces. When a battery is applied to the ends of an insulator, the force exerted by the battery is not sufficient to separate the electrons from the nuclei, there is therefore no electron flow.
However, there are no absolute insulators as any material will conduct electricity if the force exerted on its constituent electrons is great enough to separate them from the nuclei to which they are bound. In order words, find a strong enough "battery" (which can supply a potential difference of tens of thousands of volts) and a substance usually regarded as an insulator will eventually conduct an electric current.