广寒宫 is central to one of China's most beloved myths: the story of Chang'e Flying to the Moon (嫦娥奔月, Cháng'é bēn yuè). According to legend, the archer Hou Yi was given an elixir of immortality. His wife, Chang'e, drank it to protect it from a thief. Instead of becoming a goddess on Earth, she became so light that she floated all the way to the moon, where she has lived ever since in 广寒宫, accompanied only by a Jade Rabbit (玉兔, Yùtù) who pounds the elixir of life. This story is the cultural cornerstone of the Mid-Autumn Festival (中秋节), one of the most important holidays in the Chinese calendar. On this night, when the moon is at its fullest and brightest, families gather to eat mooncakes (月饼), gaze at the moon, and tell the story of Chang'e in her lonely palace. The palace, therefore, symbolizes reunion (as families gather to look at it) and separation (as Chang'e is forever separated from her husband).
While it is a mythological term, 广寒宫 is still very much present in the modern Chinese imagination.