The Egg Moon
This has nothing at all to do with Easter Eggs!
We see a full moon each month of the year. The April full moon occurs on April 11th. They all have their own names, these can be linked to seasonal changes and can be dated back to the monastic period of history from the 8th century.
April sees with the lengths of daylight increasing and the temperature getting warmer, which means people who keep free range Ducks,Hens and Geese will see them start to lay more eggs.
The monks would have kept these birds and would have been aware that April would have seen the increase in the number of eggs being laid, hence the name of the April Full Moon, the Egg Moon!