Short answers, pulled from the story.
William Baumol published his formal definition of natural monopoly in 1977 within the American Economic Review. He described it as an industry where multi-firm production costs exceed the cost of production by a single monopoly.
Railways demonstrate natural monopoly characteristics through the prohibitive cost of laying tracks and purchasing trains. Telecommunications networks require building poles and growing cell infrastructure at expenses too exhausting for competitors to match while electricity grids need cables and water services demand pipelines whose construction costs prevent existing competitors from entering the public market.
John Stuart Mill wrote about these concepts decades before the marginalist revolution took hold in economics. He argued that skilled labourers enjoy what he termed a natural monopoly against unskilled workers and later applied the term to capital itself noting businesses requiring large capital limit who can enter those employments.
In Bolivia's 2000 Cochabamba protests a firm with a monopoly on water supply excessively increased rates to fund dam construction. Many residents could no longer afford this essential good after price hikes driven by unregulated monopoly power.
High infrastructure costs create barriers that make competition inefficient rather than beneficial. A company with high fixed costs needs many customers to earn a meaningful return on investment as output increases those initial investments are divided among more users lowering the unit cost for each customer.