Rebirth
There are many ways of looking at rebirth.
Existence Manifesting
Ultimately, it is Existence (God, Buddha Mind, Big Mind) expressing, manifesting and exploring itself as and through a living being.
From this view, we see that everything - every phenomena - is the incarnation or rebirth of Existence. And that Existence is continiously reborn in the present, dying as what it was and reborn as something else.
Drop Big Mind
A level down, we see that it is the small, local drop Big Mind functionally centering on another living being, another emissary into the world of phenomena. It is, as many has said, just like taking off a worn coat and putting on another one.
Patterns
And at another level, we see that there may be habitual patterns (of emotions, thoughts, behavior) continuing between the death of one organism and the birth of another. This is the "traditional" new agy view in the west, although somewhat dubious.
Of course, if we are exclusively identified with our human self, this is the only view of rebirth that makes sense. If we are not, this is maybe the least interesting (although has some practical value, if accurate).
To clarify here: If we are exclusively identified as our human self, then we see it as "I" being reborn. When we awaken as Big Mind, we see that it is only patterns being reborn - just vortexes in the seamless whole of phenomena. "I" am either pure awareness (when still attached to the thought "I") or "I" am the whole of existence as it is.