What is the true meaning of the word "roger" when used on the radio? What is its origin?

Question

When pilots learn to talk on the radio they can generally learn that the word "roger," when used on the radio, is a way to acknowledge that a message was received. What is the textbook definition of the meaning of this word when used on the radio? Also, what is the origin of this word?

Answer 1

In the US, the "textbook" meaning is in the Pilot/Controller Glossary:

ROGER − I have received all of your last transmission. It should not be used to answer a question requiring a yes or a no answer.

The AIM 4-2-3 gives an example of using it to acknowledge instructions:

Acknowledge with your aircraft identification, either at the beginning or at the end of your transmission, and one of the words “Wilco,” “Roger,” “Affirmative,” “Negative,” or other appropriate remarks; e.g., “PIPER TWO ONE FOUR LIMA, ROGER.”

As a counterpoint to that, when I first learned to fly in South Africa I was told never to use Roger in transmissions because it doesn't tell the controller anything useful (obviously the FAA disagrees).

And as for the etymology, that's already been covered in another answer:

This usage comes from the initial R of received: R was called Roger in the radio alphabets or spelling alphabets in use by the military at the time of the invention of the radio

Answer 2

The word "roger" is used to acknowledge that a message was received, and goes back to the early uses of radio. From Wikipedia:

This usage comes from the initial R of received: R was called Roger in the radio alphabets or spelling alphabets in use by the military at the time of the invention of the radio