Natural monopolies are allowed when a single company can supply a product or service at a lower cost than any potential competitor, and at a volume that can service an entire market.
They can charge higher prices and make more profit than in a competitive market.
The can benefit from economies of scale – by increasing size they can experience lower average costs – important for industries with high fixed costs and scope for specialisation.
One of the most promising ways in which competition can sometimes be efficiently introduced into industries that are characterized by natural monopoly is for competing firms to be allowed to provide goods or services via the same infrastructure, i.e., a form of common carriage.
Sometimes a monopoly is necessary. It ensures consistent delivery of a product or service that has a very high up-front cost. An example is electric and water utilities. It's very expensive to build new electric plants or dams, so it makes economic sense to allow monopolies to control prices to pay for these costs.
A natural monopoly occurs when the most efficient number of firms in the industry is one. A natural monopoly will typically have very high fixed costs meaning that it is impractical to have more than one firm producing the good.