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The word is also used in radio communications to indicate receipt of a message. From around 1938 it was the military phonetic for the letter "R" abbreviation for "Received," later replaced by "Romeo."
In the old days of radio when Morse code was still used, radiomen used the letter "R", dot dash dot (di-dah-dit) as a quick way to transmit acknowledgement of transmissions or as a "yes." When voice radiotelephony was developed, the old radiomen stuck to the "R" as meaning yes. Since the phonetic alphabet for "R" then was Roger, the carryover was a natural logical development.
It is still used today in military parlance to acknowledge the receipt of a command or orders, i.e. "Roger, returning to base" or "Roger, Wilco or "Roger, that"." With the widespread use of cell phones and SMS (Short Message Service) or "text" messaging, Roger is slowly being replaced by "K" for OK outside of military use.