| Radio waves are are electromagnetic waves with a frequency between roughly 100KHz and a few GHz. (electromagnetic waves of higher frequencies are, in sequence: microwaves, infrared waves, visible light, ultra-violet waves, X-rays, gamma waves). In the wave theory, they are an oscillating electromagnetic field. In the quantum theory they are propagating photons. The higher the energy of the photon, the higher the frequency of the wave. The difference between the two theories is academic and beyond the scope of this article.
Electromagnetic waves originate when electrons are accelerated (or slowed down, or change direction, but mathematically that makes no essential difference). Specifically radio waves originate when electrons move forth and back in the transmitter's antenna (this is the electrical current that is fed to the antenna).
Electromagnetic waves travel freely through (empty) space. Depending on their frequency, they also travel more or less easy through a variety of matter. Air is transparent for most of them, while metals will stop most of them.
When (radio)waves reach the receiver's antenna, the process is reversed making the electrons oscillate in the rythm of the waves, which is the electrical current that is used as input for the receiver. | 
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