Electricity is the movement of from one atom to another along a conductor.

The sentence can be completed as follows:

"Electricity is the movement of charges from one atom to another along a conductor."

The movement of the the charges is due to the presence of a potential difference across the conductor, which pushes the charges. More specifically, in normal conductors, the carriers of electricity are the electrons. Therefore we can rewrite the sentence as

"Electricity is the movement of electrons from one atom to another along a conductor."

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