Transcriptions were records in 10, 12, 16 inch diameter size, made of acetate. Before the invention of audio tapes, they were used to record radio shows and programs. Played at 33 1/3 rpm a 40 cm disc could store about 15 minutes of talk, music, or whatever. The time needed to turn the records commonly was used for announcements, commercial breaks or to play station "jingles".
Apart from discs which contained whole programs, there were also records containing music only. In this way (remember - one side of a transcription disc could store about 15 minutes of recording, which were about 5 music tracks) stations could set up giant music archives, thus being able to satisfy listeners request shows without having to keep thousands of single records in stock. Those achrives were called "Library Programs" then.
It needs mentioning though, that the transcription discs were no invention of the Army, but were invented in the 1930s in the States to enable all the radio stations to build up programs without having to buy and store many, many records. The transcriptions were produced by so called Transcription Companies and then shipped to the radio stations in the whole country. The stations did not have to pay when they received the records but when they played them.