Verse 2

2. All this,  verily,  is the Absolute. The Self is the Absolute. This Self,  such as it is,  has four quarters.

" All this,  verily,  is the Absolute".

We have as a description of reality from the scriptures that The Absolute,  Brahman,  God,  alone exists.  It naturally and logically follows that  "All this... is the Absolute".
Even this transient and mortal universe is  "the Absolute"  because it is formed of the immortal knowledge and consciousness that is the Absolute.  All of this is Absolute Knowledge manifest,  (but the Absolute is greater than this manifest experience,  this unknowable infinity will be described as the fourth quarter).

"The Self is the Absolute".

The word  "Self"  conveniently describes the experiencing of the projected manifest forms of creation,  particularly sentient beings.  In reality all names and forms exist purely as knowledge within Non-Dual Absolute Consciousness.
In truth it is within Absolute Consciousness that all experience takes place.  No actual  "Self"   exists as an entity,  (because The Absolute or God alone exists).
The  "Self"  is merely a convenient description for the experience of desire within this duality,  witnessed by the Absolute through Maya.

"This Self,  such as it is,  has four quarters".

So,  this  "Self",  is merely a linguistic convenience  ("such as it is")    for describing the created or projected forms of Absolute knowledge.
Being created,  the Self is mutable,  it appears to have changes of states,  sleeping waking dreaming and so forth. These states are experienced as states of consciousness,  as it were,  they are named and described here through  "four quarters"

The four quarters are not meant to be taken literally of course.
The imagined four quarters are for the exposition of Om and  "Self"  Consciousness only.
All This Self or Om is the Absolute,  but the Absolute is more than all This.  That the Absolute is more than Om or the Self,  needs to be held in mind while considering the "four quarters".  The fourth  "quarter"  is in fact the one eternal Absolute reality,   it is the Non-Dual Consciousness within which the first three transient mortal quarters are held,  as it were.
The meaning is that the described states are merely experiences that appear on the one unchanging Consciousness Absolute.  The fourth state is the eternal reality that remains after the cessation of the three transient states.  In reality no  "state"  exists,  there is just Consciousness Absolute.