Purple moon is the special name given to the second full moon of April. Generally, second full moon in a month is called the blue moon. The full moon occurring in April is called the Pink Moon, along with an array of different names. Purple Moon would fit well as the name of second full moon in April following Pink Moon as the first full moon, analogous to mixing pink and blue yielding purple. Giving that April has only 30 days while most other months last 31 days, blue moon in April is extremely rare, which led to the idiom 'once in a purple moon' referring to an extremely rare event, even rarer than the more familiar 'once in a blue moon'.
In the Central Time Zone where I live, the last purple moon occurred in 1942, before that it occurred in 1923, and the next purple moon will occur in 2045, followed by 2064, then 2075. Though in New York time, the last purple moon occurred in 1961 as full moon time was 11:48 PM CT on March 31, 1961, only 12 minutes shy of April 1, but in New York it wouldn't occur again until 2064 as purple moon occurs at 11:52 PM CT on April 30, 2045. For much of Europe, Africa, the Middle East and Asia, the last purple moon occurred in 1999, but for those regions up through Middle East, the next purple moon would not be until 2075. For far eastern world like Japan and central and eastern Australia, the last purple moon occurred in 1980 and will next occur in 2094.