That's when the leaves are freshly out and it is safe to plant new seedlings without fear of frost. On Little Cranberry Island off the coast of Maine, they go with the weather, not the calendar. They have a large picnic and a May Pole dance in June to welcome summer each year. South of the equator, summer comes in the calendar months of October or November. So forget the calendars.
Summer comes to each depending on the vagaries of weather and the geographic location.
Last I heard, it was still snowing up there. Summer comes when it is warm enough to plant and to keep the animals outside. Like the Celtic shepherds, we still pattern much our lives according to the rhythms of nature. This website comes from Glasgow. It's called the Celtic Shopping Mall and specializes in things Scottish.