Because it deals with the nature of assumption. When we are aware, we assume reality.
Thus self awareness is the assumption of assumption, where one self evident truth (assumed) projects to a further self evident truth (assumed).
This had implications in not only consciousness but also the maths, sciences, religions etc. precisely because they are all built on axioms...which are assumed.
Even conceptualizing a phenomenon, ie to assume it from another angle, results in a change in that phenomenon.
A simple example would be the the principle against circularity by Peter D. Klein under the infinitism school. It is a principle that necessitates one axiom progresses to another but it never repeated. So one assumption effectively changes to another non repeated assumption and this provides a definition of "how to reason" without necessarily "self reflect"...which is circular.
However significance is contextual...again.
It is significant for AI of course, but is necessary for quantum physics in light of the paradoxes of "measuring something affects it" which you can Google and get a load of interpretations...which goes to basic questions of how we derive self evident truths all together in the scientific method. You can read popper for the question of science.
Also googling manly P hall, point line and circle will give some clarity as to the nature, hence importance of self reflection.
Basic self reflection begins with apriori concepts (read further into kant). The most basic is the point. (M.P. Hall).
Considering we observe through apriori concepts we effectively reason through them. Space and time is the most subject of them all (kant, Augustine).
So in assuming oneself we effectively are assuming a point of awareness. This is represented by a simple point. In assuming this state of awareness we create a new self, a new perspectivd... quite literally a new point of awareness.
This can be observed in our basic conception of time, the grounding for subjectivity, as represented by a line between to points (as observed by Heidegger in being and Time).
One subjective self, with the most subjective assumption being a simple point, in reflecting upon itself effectively individuated itself into another point of awareness.
This is the foundation of definition...one point directed to another point with each point not only representing a self as point fo awareness but also a measurement in empirical reality where we pick a point of reality and measure from it. Euclid observed this in his first postulate but never elaborated much on the psychology of it.
The pyrhonists observed this inherent dissent of one point of view to another, in agrippas trillema.
So the dividing line whic literally is the progress of one set of assumed truth to another and we are left with the many different school and sciences...and further confusion.
Platonic forms, specifically the line between two points, can be observed as the foundation of self reflection as having an inherent form. Considering Plato himself set up the argument of Justifed true belief, one could argue that the forms are strictly "the way we reason".
This can be observed in the forms of linear and circular reason we use to define any assumption we make as well as this assumption merely being a "point of view" in itself.
Hopefully this will give some food for thought, I may have to clarify some points further.
But the paradox is that self reflection is the act of definition.