The sufi whirling is performed by dervishes of the Mevlevi order. It is a dance by the devout that depicts their ecstasy.
The performance is part of a sama, where musicians play sufi music. This photograph was taken during one such sama at an event in the Sirkeci railway station hall at Istanbul.
More photographs in comments section.
To know more about Sama' (sema) you can read the wikipedia entry on it here