From the Old Farmer's Almanac web site: April’s Full Moon, the Full Pink Moon, heralds the appearance of the “moss pink,” or wild ground phlox—one of the first spring flowers. It is also known as the Sprouting Grass Moon, the Egg Moon, and the Fish Moon.
These names were not invented by The Old Farmer’s Almanac. They were used by early Colonial Americans—who learned the names from the local Native Americans; time was not recorded by using the months of the Julian or Gregorian calendar. Many tribes kept track of time by observing the seasons and lunar months, although there was much variability. The name itself usually described some activity that occurred during that time in their location.