舞う primarily means to flutter, to swirl, or to dance in a graceful, often floating manner.
It conveys a sense of elegance, lightness, and sometimes a more traditional or poetic quality. It is frequently used in the context of nature, such as leaves fluttering in the wind, snowflakes falling gently, or birds dancing in the air.
When referring to human dancing, 舞う often implies a more traditional or ritualistic dance, such as those found in classical Japanese arts like Noh or Kabuki.