Anatta means non-self in sanskrit. In short, this means nothing has the actual capacity to be a self, therefore it cannot be got, had, or owned, or in the event that it is, it’s not a self or thing we can call our own for it has nothing of it that has the capacity of actually being ours. This is quite a deep concept, for it explores that nothing in it’s pure form has the capacity to be a self.
A toy made of wooden block cut at specific angles and retrieved off of a shelf to play. It cannot be mine for it has no self that I can acquire and put into my possession. A person made of blood, skin, bones, and thoughts, how can that person become mine? How can it become my property so much so that I can call it mine?
Futher, and perhaps easier to gain insight with, the struggling and striving we undergo to acquire this thing so that we can call it ours as if it is a thing that becomes us, surely it is easy to how this exists in our own lives. My phone, my table, my house, my car, my clothes.. I have consumed each of these and declared them mine. Do you have some things in your life you call yours?
When combined with unsatisfactoriness and impermanence of things, we can begin to see how all of life is suffering, therefore suffering is life. We can begin to see why the Buddha stressed more than anything else that the disillusion of these Three Universal Truths can lead one towards peace.