A Sunshine Girl (天気の乙女 Tenki no Otome , lit. "Weather Maiden") is a maiden who has been granted weather-changing powers.
As described by the priest that Keisuke Suga and Natsumi Suga visit, the Sunshine Girl theory began as a folklore from ancient Japan. It tells of a weather maiden able to change the weather according to the people's wishes, and one would be born into every village each generation. The drawback of this wonderful power, however, was that they would eventually begin to disappear the more the utilized their powers, and would be spirited away entirely once they reached a certain stage of translucency.
Using the example of Hina Amano, the modern-day Sunshine Girl, it can be deduced that this tale's lore is true, and maidens can be granted weather-changing powers.
The origin of this power appears to be the rooftop of Yoyogi Kaikan for unknown reasons, as when Hina prayed whilst she was passing the tori gate atop its rooftop shrine, she was taken into the sky. After she returned, she'd become a Sunshine Girl with the ability to make the rain clear up by praying. However, the spiriting away to the sky aspect of the Sunshine Girl origin isn't limited only to those who are Sunshine Girls, as Hodaka Morishima was able to enter the sky via the shrine's gate when he was attempting to save Hina.