Self (atta), in the philosophical sense as opposed to it's conventional usage, is defined as that which is "permanent, stable, eternal, not subject to change" (SN 24.3). Our sense of self, the ephemeral "I," on the other hand, is merely a mental imputation, the product of what the Buddha called a process of "I-making and my-making."
In the simplest of terms, the Buddha taught that whatever is inconstant is stressful, and whatever is stressful is not-self—with the goal being to essentially take this [analytical] knowledge, along with a specific set of practices such as meditation, as a stepping stone to what I can only describe as a profound psychological event that radically changes the way the mind relates to experience. That doesn't mean, however, that the teachings on not-self are understood to deny individuality () or imply that the conventional person doesn't exist (). The way I understand it, they merely break down the conceptual idea of a self — i.e., that which is satisfactory, permanent and completely subject to our control — in relation to the various aspects of our experience that we falsely cling to as "me" or '"mine'" ().
So in essence, the Buddhist teachings on not-self aren't merely assertions that we have no self; they are a method for deconstructing our false perceptions about reality, as well as an important tool in removing the vast net of clinging that gives rise to suffering.
This may be a bit of nonsense, but in one of the ways I like to look at it, the conventional viewpoint (sammuti sacca) explains things through subject, verb and object whereas the ultimate viewpoint (paramattha sacca) explains things through verb alone. In essence, things are being viewed from the perspective of activities and processes. This, I think, is incredibly difficult to see, but perhaps what happens here is that once self-identity view (sakkaya-ditthi) is removed, the duality of subject and object is also removed, thereby revealing the level of mere conditional phenomena, i.e., dependent co-arising in action. This mental process is "seen," ignorance is replaced by knowledge and vision of things as they are (yatha-bhuta-nana-dassana), and nibbana, then, would be the "letting go" of what isn't self through the dispassion (viraga) invoked in seeing the inconstant (anicca) and stressful (dukkha) nature of clinging to false refuges that are neither fixed nor stable (anatta).
"Sabbe dhamma nalam abhinivesaya" ().
(non-Buddhist related blog)