Anatta is the view that there is no enduring self. All phenomena are conditioned--have a begining and an end--so there is nothing to which they can attach. Suffering arises from the illusion that impermanent conditioned states are permanent and can be posessed by a 'self'.
Moreover, there is no self or soul which carries on after death. Instead we are merely a collection of groups of grasping (or khandha) which are in a continual state of flux. Rebirth is possible only because we are driven by our desires and volitions.