Kagura is a wind demon. Using her fan she has the ability to manipulate the wind and corpses in order to attack her enemies.
Dance of Blades/Fuujin no Mai
This is Kagura's main attack. Using her fan she has the ability to fling wind blades to injure her opponent. Later she uses them to hold off an enemy so she can escape without actually having to fight (usually with InuYasha).
Dance of the Dragon/Ryuuja no Mai
With this attack, her fan conjures swirling tornadoes, which can be used to trap an opponent. It can also prevent InuYasha from forming his Wind Scar/Kaze no Kizu.
Corpse Dance/Shikabane Mai
This attack allows Kagura to manipulate corpses. She can control them until they are no longer useful, then she "releases them" and they dissolve.
Feather
Kagura uses this for transportation. She removes a feather from her hair and enlarges it so that it can fly.