This is the "international phonetic alphabet" as used in military radio communications and aviation in order to spell out words. (It is not, of course, a "phonetic alphabet" in the sense that a linguist would use.)
Older version (to WW II)
Current version by International
Civil Aviation Organisation (1955)
There have been many other similar alphabets (see Brian Kelk's pages), and they exist for many languages, not just English. Most people, however, invent their own on the fly, often using proper names, J as in JIM, E as in EDWARD, etc.
Readers of Arthur Ransome's children's books will remember Uncle Jim's angry conversation with the telephone operator when he tries to alert the firefighters to a fell fire in Pigeon Post, "Fellside seven-five... No, not NINE, FIVE... F for FOOL, I for IDIOT, ..."