According to the Farmer's Almanac, the June full moon was known to every Algonquin tribe as the Strawberry Moon because it signified the start of the strawberry harvesting season:
It was often known as the Full Rose Moon in Europe (where [modern] strawberries aren't native).
The June full moon is also sometimes referred to as the "hot moon" since it marks the start of warm weather in North America. ~snopes.com