The full moon of May is often known as the Flower Moon or Mother's Moon. It is the month where the Earth flourishes. Plants, animals and insects all come into their prime as summer approaches, and the Earth changes from her Maiden form to her Mother form.
The beginning of May is marked by the festival of Beltane or May Day, which celebrates the great marriage between the Earth and her lover to allow this life to flourish.
A lot of plants come into flower this month, hence the moon's other common name. This is explained by another county saying:
April showers bring forth May flowers.