Wind is the fourth of the five Japanese elements, Earth, Water, Fire, Wind, and Akasha. In Japanese culture, wind represents things that "grow, expand, and enjoy freedom of movement." Besides for smoke and air, wind fu can also represent the human mind. This means that as we grow physically, our mind and thoughts expand as well in terms of knowledge, experiences, and personality.
As we know, one of Kagura's attacks starts with Fujin, which is actually the name of a Japanese Wind God. He is one of the eldest Shinto Gods in the story books who is portrayed as a terrifying wizard-demon that holds a bag of wind over his shoulders. The iconic wind god seemed to have its origin along the Silk Road trade that fell through myths and folklore. The image of him has changed over time, but he's always kept the silk bag over his shoulder throughout it's evolution.
Element manipulation, also known as elementalism, is when a user can create or shape a basic element on the Earth. Kagura is able to use this power to specifically manipulate the air and wind around her and other objects. This allows her to shape and manipulate the air in many different forms including tornadoes, hurricanes, vertical drafts, micro-bursts, and other devastating forms of wind.
Kagura doesn't just use the wind around her, she sees her soul as the wind. When she dies in the Final Act, her soul yells out "I am the wind. The free Wind." Kagura had the mindset of wanting and craving to be able to roam free through out the sky. She loved using her Plume and floating in the wind above the world itself. However, while being under control of Naraku, she couldn't be free like she had been craving. Only in the death of her physical being could her soul fly free into the wind.