The name does refer to worms, as they tend to emerge from the soil around this time of year. The “super” part refers to the fact that the moon happens to be full at the point in its orbit where it is closest to Earth, which will make this weekend’s show quite easy to see for people blessed with a clear sky.
The “Worm Moon” name first appeared in the 1930s Maine Farmer’s Almanac, which started publishing moon names for each month of the year. According to the almanac, the full moon in March was variously called the crow, crust, sap, sugar, or worm moon.
The next full moon will occur on April 26, and is called a pink moon. It’s also considered a supermoon. 
A version of this article was previously published on March 20, 2019, and was updated on March 26, 2021, with more information.