An electric appliance is powered by electricity which is basically flow of electrons.
Electron flow Powers your appliance. Think about it this way, something which is stationary(at rest) needs some kind of force to be applied externally to move.
Electrons provide that force(push) in the form of current. Which is basically electrons getting pushed around by voltage(potential difference) to push something else to move.
Another nice analogy would be a hydroelectric powerplant’s turbine moving because its is being pushed by the force of the moving water.