I think the issue is about how the waves actually carry the information.
The answer involves the idea of 'modulation'.
If you flash a light and send a message using Morse code, you are transferring the information by modulating the light beam on - off etc.
The simplest radio transmissions consist of bursts of a radio wave. The transmitter is simply keyed on and off, using morse code or some other 'binary code' modulation that the distant receiver / operator can recognise. This was called 'wireless telegraphy', which was used in a similar way to 'telegraphy', which had to use wires on telegraph poles, between towns.
If you just connect the output from a microphone to an antenna, nothing will happen. The waves produced by the antenna just wouldn't propagate through the air / space because the frequencies involved are only a few kHz (1000 oscillations per second).
For decades, speech and music has been sent, using Amplitude Modulation. of a radio wave (A.M.).
A carrier wave at a frequency that will propagate through space - usually way above 1MHz (1,000,000 oscillations per second) is transmitted. By modulating the size (or amplitude) of the carrier wave in step with the electrical voltage from, for example, a microphone, the signal from the microphone is carried to the receiver. The receiver is 'tuned' to the wanted carrier frequency (rejecting all signals at other frequencies) and detects how the received wave is modulated. The detected voltage varies in the same way that the original microphone signal varied and it can be heard with an earphone or amplified and fed to a loudspeaker.
This allows the information to be carried from A to B and also, by using carrier waves of different frequencies, many signals can be transmitted and received at the same time, as long as they are separated in frequency (each channel needs 'bandwidth').
There are many other methods of modulating a carrier wave; altering its frequency, pulsing it with high speed digital signals or by changing its phase etc.. In all cases, the term 'carrier wave' describes just what happens - a low frequency signal is carried by modulating a high frequency, transmittable, wave.
What a bit of luck - without it we'd have no Radio 4.
Of course, transmitting TV pictures has a whole new layer of complication on top of this. . . .