"Mayday" has nothing to do with the first of May. It's an anglicised version of the French expression m'aidez or m'aider, literally "help me!"
According to convention, in an emergency the expression is repeated three times for absolute clarification.
While it has the same meaning as S.O.S. – "Save our Souls" – "Mayday" is more commonly used to convey an emergency verbally. S.O.S. is used less often these days since it was used mostly to indicate an emergency situation when transmitted by Morse code – three dots followed by three dashes and three more dots.
After the sinking of the Titanic S.O.S. became the standard emergency signal for ships' wireless operators transmitting via Morse code. Previous to that the emergency signal was "CQD" – "all stations: distress." Since S.O.S. is more difficult to understand when spoken, Mayday is the preferred option for voice communication.
However there is still life left in S.O.S. Should you ever find yourself stranded on a desert island, or in a snowy wilderness, stomping out S.O.S. makes your situation crystal clear to anyone passing by or flying above.