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That is related to the fact that the electrical forces are basically transmitted at the speed of light. This allows the current in a wire to travel at about 2/3 the speed of light in a vacuum, despite the fact that individual electrons move much slower than that (and the drift speed of a current is typically less than a millimeter per second). What happens here is simply that one electron (or other charge-carrier) transmit the energy to the next one, via electrical forces.

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