The Great Summer, also called the Long Summer, is a fabled summer that never ends. It is supposed to be sent by the gods when all men are good. When there is a long summer, it is often hoped that the Great Summer has come. The smallfolk believe a long summer means a longer winter.
A Game of Thrones
Grand Maester Pycelle reminisces to Eddard Stark about King Maekar Targaryen's summer, which occurred when Pycelle was a young man still forging his chain. It was hotter than the current one, and nearly as long. Pycelle says that there were fools, even in the Citadel, who took that to mean that the Great Summer had come at last, the summer that never ends. But in the seventh year it broke suddenly, and there was a short autumn and a terrible long winter.
A Clash of Kings
A Dance with Dragons
and her triumph over darkness will bring a summer that will never end...