At the negative pole, an excess of free electrons is created, & at the
positive side a lack of electrons is created (called holes in
electronics), leaving just the protons to contribute their positive
charge.
The extra electrons in the negative terminal try to push other electrons
away or move themselves away and closer to a lone proton in the
positive terminal, this due to the properties of charged particles: same
charges repel each other and opposites attract.
Electrons can't go to the positive terminal because the negative
terminal is isolated from it, or in the case of batteries, there is a
chemical reaction keeping them away. All that is left is the force of
the electrons pushing against each other, unable to meet a proton and
reach an equilibrium.
This contained force is what we call voltage.
When there is an available path through which electrons can move, they
quickly reach the holes at the positive terminal; This movement of
electrons is called current.
