Each stone varies. Blue kyanite, like the rest of the kyanites, hold a very high vibration and create rapid transfers of energy. Kyanite is really good for: Inner bridges, psychic ability, connecting with Nature, past-life recall, telepathy and empathy.
This stone helps one increase mental compacity so that they can "download" information from higher sources. Lucid dreaming will also be stimulated if one decides to sleep with the stone.
Physically, kyanite can help bridge any energetic gaps caused by the breaking of bones, surgery and other intrusive trauma. It can heal the brain from the effects of head trauma, seizure or stroke as well as aiding in creating new neural pathways around damages areas. 
Kyanite is essential for healers of any kind as it's very popular amongst Crystal Resonance Therapy.