Hertz's experiments are said to have proven Maxwell's theory correct, but how exactly did his experiment do this?
This article on the Institute for Electrical and Electronics Engineers site gives a detailed account of the history involved. For those not wishing to read the entire article, I provide the relevant points here.
Hertz’s experimental work on the subject began at the Technische Hochschule (now the Karlsruhe Institute of Technology) in Karlsruhe, Germany, in 1886. He noticed that something curious happened when he discharged a capacitor through a loop of wire. An identical loop a short distance away developed arcs across its unconnected terminals. Hertz recognized that the sparks in the unconnected loop were caused by the reception of electromagnetic waves that had been generated by the loop with the discharging capacitor.
Inspired, Hertz used sparks in such loops to detect unseen radio-frequency waves. He went on to conduct experiments to verify that electromagnetic waves exhibit lightlike behaviors of reflection, refraction, diffraction, and polarization. He performed a host of experiments both in free space and along wires. He molded a meter-long prism made of asphalt that was transparent to radio waves and used it to observe relatively large-scale examples of reflection and refraction. He launched radio waves toward a grid of parallel wires and showed that they would reflect or pass through the grid depending on the grid’s orientation. This demonstrated that electromagnetic waves were transverse: They oscillate, just as light does, in a direction perpendicular to the direction of their propagation. Hertz also reflected radio waves off a large sheet of zinc, measuring the distance between canceled-out nulls in the resulting standing waves in order to determine their wavelengths.
With this data—along with the frequency of the radiation, which he calculated by measuring the capacitance and inductance of his circuitlike transmitting antenna—Hertz was able to calculate the speed of his invisible waves, which was quite close to that known for visible light.
Maxwell had postulated that light was an electromagnetic wave. Hertz showed that there was likely an entire universe of invisible electromagnetic waves that behave just as visible light does and that move through space at the same speed. This revelation was enough, by inference, for many to accept that light itself is an electromagnetic wave.
Eventually scientists accepted that waves could travel through nothing at all. And the concept of a field, at first distasteful because it lacked any mechanical parts to make it work, became central to much of modern physics.