Short answers, pulled from the story.
Voltage is the difference in electric potential between two points. In SI units, one volt equals one joule of work per one coulomb of charge. It measures how much work is needed to move a unit of positive charge from one point to another against an electric field.
The volt is named in honour of Alessandro Volta (1745-1827), the Italian physicist who invented the voltaic pile, possibly the first chemical battery. Volta also coined the term electromotive force in a letter to Giovanni Aldini in 1798.
Voltage in batteries arises from electrochemical processes. Other sources of voltage include electromagnetic induction in generators, the piezoelectric effect from mechanical pressure, the photovoltaic effect from light, and the thermoelectric effect from temperature differences.
A voltmeter measures the electrochemical potential difference between two points by connecting one lead to each point. Analog voltmeters run current through a fixed resistor and infer voltage via Ohm's law; potentiometers balance unknown voltage against a known reference; oscilloscopes deflect an electron beam in proportion to the voltage.
Power companies in North America typically supply 110 to 120 volts AC to consumers, while most of Europe uses 220 to 240 volts AC. High-voltage transmission lines that carry electricity from power stations operate at 110 to 1200 kV AC, far above either household standard.
Voltage corresponds to the pressure difference between two points in a water-pipe system driven by a mechanical pump. Just as greater water pressure drives more flow, a larger voltage between two points drives a greater flow of electric current. A dead battery is analogous to a stopped pump that produces no pressure difference.