The first thing that goes is personal identity.
So far, our brains have been shielded well in our skulls. Our minds too have been shielded relatively well in human shells.
The human body is a nice piece of work. It has nice interfaces, simple and delineated in function: eyes, mouth, hands. (Physical delineation makes for a damn good firewall.)
Input - output. A ghost within a human body living in a human world. Reality, as well as identity, is distinctive from within the human individuality.
If you override the massive shielding with the invention of a thing like a cyberbrain, human individuality has just become a much-much more elusive thing.
The next thing that goes is the layer of human social reality.
There are some terms and phrases from the "Ghost in the Shell" universe which are used to describe possible major implications: cyberbrain sclerosis, closed shell syndrome, stand-alone complex, ghost pattern, ghost hacking, superstructure, true artificial intelligence, etc.
Many of these concepts have their non-cyber counterparts and can be used to point out these aspects.
Even if the 'real' world does not move in this direction, there are many things we could learn about ourselves by assuming 'cyberbrain existence and use' as an axiom and unfolding the possibilities that follow.
One way or the other, the implications of cyberbrain use are present in the 'real' world to a degree and are here to stay.