Why is there only one Twitter? One centralized phone network?
A natural monopoly is a business that benefits its users by being the one and only. If there were two incompatible phone networks, you'd need access to both in order to call the people in your life–and remember who was on each network.
Metcalfe's Law states that the power of a network goes up with the square of the number of people using it. In networks, then, there's a real penalty to having a second one.
An expensive shared resource (like power lines) are also a natural monopoly, since the incremental cost of adding one more user to the first line is so much less than the cost of building a second one right next to it.
It's possible to transform a service that might not be a natural monopoly (an app that helps you track your workouts) into one that might be (an app that lets you share your workouts with others).
Many natural monopolies exist in the micro space, as opposed to being universal monopolies used by one and all like the telephone. We only 'want' there to be one trade show for our industry, one trade association, one certification board.
Over time, even natural monopolies fade away, but when you look for breakthrough new projects (particularly as an investor) the home run lies in discovering the next one.