Ignorance is a word for the universe before it developed Mind with its ability to discriminate, recognize, judge, separate, and set goals.
Most of the Twelve Nidanas describe development and taking shape of the above qualities and corresponding representational experiences.
The naive mind, as it develops, delineates entities, calls some of them desirable, designates the logical center of experience as "self" and engages into purposefull action to get this self in position to acquire the desirable entities (and other experiences).
Rebirth refers to the tendency of this process to cyclically recreate itself despite the limitations of physical media.
"Birth" specifically refers to the birth of "self" as the designated center of experience and action. The way the birth of self depends on craving for entities and on the purposefull action, is described in the Twelve Nidanas. Basically, our perception of distinct entities develops in conjunction with taking shape of our like/dislike attitude which eventually matures into Self based on the mental fabrications we engage into on the way to acquiring capacity for purposeful action towards the desirable entities.
It's not really an anthropocentric view, it is representation-centric and information-centric, with media playing secondary role.
Uprooting ignorance refers to clearly understanding (and seeing in one's own real life) how this process works. It has an effect of dispelling the illusion of solidity that depends on not understanding the mechanisms behind the magic trick.
To say that rebirth has ended is a simplification though, because technically the process at large still goes on, you just no longer identify with any part of it. So for you it's the last birth because now you know there was no you ever, to begin with. But for others it still continues. The tendencies that led to your Liberation/Enlightenment do not completely disappear though, which is why in Mahayana we say that enlightened Bodhisattvas keep on existing in some sense, helping new students from the realm of subtle elements.