-The question cannot be answered correctly with providing an interpretation that effectively is always an extension of the one. Thus each interpretation is a variation of the one.
-You will have to meditate and figure it out for yourself. However a few clues can be observed. No academic source can accurately clear this statement.
-You will not observe an accurate interpretation as Plato himself claims that Philosophy cannot be limited to written language without doing harm (c).
I bring these three points up because one must look at it through the premise of Parmenides himself and Plato, considering he was heavily inspired by Parmenides,at minimum, through Socrates.
If you look at the reasoning of Parmenides it is fundamentally circular:
Mind --> ((((Man --> Organs) --> Man) --> Mind) --> Organs) --> Mind)
Which represents each proposition as a fractal of the 1 mind, but the one mind itself existing through the many degrees. Each relation, as circular, observes the mind as circular and self reflective. It is circular reasoning within circular reasoning, a fallacy by any modern standard.
However This correlates with Platonic forms precisely because it is the underlying form of the argument. Forms as variations of the one can be seen in Platos premises as Plato was inspired by Parmenides (D). Thus understanding Platos premise may help in understand Parmenides statement.
This reflects further with the universal "form" of circularity in reasoning observed by agrippa the pyrhonists trillema (f).
Agrippa was a pyrhonist, with the pyrhonist dogma claiming all is fundamentally image (g). This philosophy was thought to be inspired by interactions with buddhism during Alexander the Greats exploits (g).
The circle was a symbol for enlightenment or nirvana in some sects of buddhism, specifically "zen". It is called the "enso"(h)
The enso was a result of a practice in calligraphy meant to occur naturally when the mind was set "free". This is interesting because it reflects an inherent intuitive base for the forms which Plato also argues for, agrippas trillema, and the inherent "circle within circle" way parmenides presented the poem.
Thus a link between pyrhonist "image", platonic form, and buddhism can be implied where the perfection of the circle can be used as a symbol for the "one" of parmenides.
This is implied however.
The circle can be observed as the most perfect of forms, thus why parmenides poem "may" follow such a framework. This perfection is describe in Platos seventh letter (c) as well as his theory of forms (d).
However if looking at the circularity of the way the poem is written: the statement is absurd, precisely because of the damage words do in philosophy as stated in the beginning (as Plato point out).
The statement is meant to be absurd precisely because each word is a variation of the one and can be connected in any way. Of using parmenides stance. We can see this if strictly taking parmenides basic assumption of all is 1. The pythagoreans viewed one as both odd and even, thus not really describable (e).
However considering the above implications presented, the reason I say it is "meant" to be absurd is that it takes on a form of reasoning similar to a zen koan.(i)
Zen koans where meant to break false reasoning, cause the student to think, and to observe the failing of words to describe reality...much like Platos statement about writing and the trillema of agrippa observe.
This may sound like a play on words, but it is inherent within his philosophy. (A) Thus the question can be answered a variety of ways without contradiction, however this leads to obscurity when taken out of context as each interpretation is a point of view that is self reflectory as an extension of the one which exists through itself alone (k)
The truth is that noone really know what parmenides meant without making an assumption. Plato and many other philosophers are just as confused as you/we are. (B)
Reality, much like the platonic forms, begging portion of agrippas trillema and zen literature...must be assumed as is...thus the poem is strictly an assumption that reflects what the observer sees from there angle of awareness.
This answer is food for thought more than anything.
(A) Encylopedia Britannica.Com, Parmenides
(B) Internet Encylopedia of Philosophy, Parmenides, 3rd paragraph.
(C) Seventh Letter, Wiki, "Long Digression on Forms" 341b-345c
(D) theory of forms, wiki
(E) Manly P Hall, "Secret Teachings of All Ages" Section on Pytjagoras and Numbers, sacred texts archive
(f) agrippas trillema wiki
(g) pyhronism, wiki
(H) enso, wiki
(I) zen koan, wiki
(K) the book of 24 philosophers, google