It is about establishing three-dimensional model of the mind. Such models differ between schools. For example, Theravada or Yogacara have many more dimensions to it described.
First dimension is the ordinary mind (psyche), it is equivalent of chitta. It is the dualistic mind responsible for Self-personality grasping. This part is also your base of imagination, rational thinking, intellectualisation. This dimension is switched off when we sleep or are in the coma, or dying.
Second dimension is substrate consciousness that is equivalent of alayavijnana which is storehouse consciousness in Yogacara school, or in Theravada, this corresponds to bhavanga. Storehouse consciousness is essentially your subconsciousness - it always processes information no matter what. It also stores everything, biologically (from your father), and experientially (past actions). Relation with chitta is that chitta allows you to transform and store good or bad seeds back into the storehouse that will one day blossom and re-manifest in psyche again. It is the relative vacuum of consciousness.
Lastly, bare awareness, primordial awareness that is Rigpa. It is equivalent to experiences of Buddha nature or wisdom of Dharmadhatu, or Dharmakaya, also Tathata or even Jhana. Rigpa is based on intuition (jnana as opposed to prajna) coming from touch with suchness. This is seeing things as they are. There are many terms that describe it. For Dzogchen practitioners, the whole singular experience of it is best seen as last remnant after two other layers dissolve at the time of death - the clear light. It is the absolute vacuum of consciousness.
Each one of these layers goes deeper and such is the relation between them, each one emerges from the lower layer. Concepts arise from being in touch with suchness and so on.
Alan Wallace's commentary on Vajra Essence:
For clarification let’s refer to the three-tiered model of the mind
presented earlier. The first and most superficial level is the psyche,
in which thoughts, fantasies, images, and so forth appear. If you sit
quietly and watch your mind, the phenomena you observe manifest in
your psyche. We access the second level, the substrate consciousness,
in deep sleep, the blackout period of death, and in the practice of
shamatha. During shamatha meditation the phenomena observed do not
necessarily emanate solely from the psyche, which is encapsulated
within this lifetime. Having accessed the substrate consciousness,
there is the potential for tapping into memories from past lifetimes, phenomena entangled within a vast network of experiences. These may appear in the form of dreams, visions, desires, or fears whose origin is not to be found in this lifetime. In the case of fear, for example, the anxiety may be very real, yet its origin may be a past-life experience. Such fear is an expression of imprints stored in the substrate consciousness.
Then, having broken through to the third tier of the mind—primordial
consciousness—what emerges, the phenomena that appear, are not
manifestations of mind and mental processes. From this deeper vantage
point, such manifestations and mental processes, which comprise the
psyche, are surface phenomena. For the same reason it would also be
misleading to depict these primordial experiences as manifestations of
the substrate consciousness. Appearances originating in primordial
consciousness are the spontaneous, natural effulgence of pristine
awareness. Being neither the mind nor mental processes, “these
appearances are by nature the play of the manifest space of
For example, if you truly fathom the
nature of anger as it arises—even something as slight as a mild
irritation—it is seen to be nothing other than an expression of
pristine awareness. Of course we don’t normally do that. We grasp on
to anger, reify it, and then act out within the sphere of the psyche
and of ordinary appearances, in which case anger is an afflictive
emotion. Therefore, if you fathom the nature of the mental
processes—the eight kinds of consciousness—it is seen that they have
never been anything other than expressions of primordial
consciousness. However, not fathoming their nature, they are then seen
either as expressions of the substrate consciousness or expressions of
the psyche, indicating that you are locked within samsara.
You can clearly see there is nothing special that cannot be experienced outside Dzogchen and that same experience is also spoken of in Mahayana in great detail.