Where does the word "mayday" come from?

Mayday has nothing to do with the first of May. It is French, respelled so an English speaker would say it right.

The problem it solved was acoustic. By the early 1920s, ships and aircraft had SOS, the Morse code distress signal. But pilots were starting to use radio telephones, speaking rather than tapping. Over a crackling voice link, the letter "S" was very hard to make out. A spoken distress word was needed.

In February 1923, The Times of London announced that "S.O.S." would give way to "May-day," the phonetic equivalent of the French "M'aidez," meaning "Help me." Grammarphobia quotes the article. Wikipedia says the new word came into use for cross-Channel flights that month.

Why French? Much of the air traffic from London's Croydon Airport went to Le Bourget, near Paris. A word that both French and English crews would recognize made sense.

The Times spelling, m'aidez, is not quite grammatical French. As Word Histories points out, m'aidez only works with vous, as in vous m'aidez, "you help me." It is not a command. The OED, as quoted by Grammarphobia, explains the source as m'aider, either used as a command or short for venez m'aider, "come and help me." A French speaker in trouble would more naturally say aidez-moi. The radio word was chosen to be heard, not to be correct.

The coinage is usually credited to Frederick Stanley Mockford, a senior radio officer at Croydon. Wikipedia repeats that story, and so does the National Maritime Museum in Cornwall, as quoted by Grammarphobia. Word Histories cautions that the attribution has never been properly substantiated. The French source is solid; the individual inventor is less certain.

The 1927 International Radiotelegraph Convention made mayday the official radiotelephone distress call, alongside SOS for Morse. Today it is said three times in a row: "Mayday, mayday, mayday." Radio also has a lesser call, pan-pan, for urgent situations that are not yet life-threatening. That one is French too, from panne, meaning a breakdown.

SOS, by contrast, never stood for anything. It was adopted internationally in 1906 as a distinctive Morse sequence, and "save our souls" was attached later.