What is the quotation's relevance to the text and its importance among general views of literature, the text, or the author Edgar Allan Poe in The Philosophy of Composition:
"Regarding, then, Beauty as my province, my next question referred to the tone of its highest manifestation - and all experience has shown that this tone is one of sadness."
Essentially what does it mean and how does it fit into the work contextually?
Oh, the quote you provide is incredibly appropriate to the context of "The Philosophy of Composition"! Why is this? Because the entire point of Poe's "The Philosophy of Composition" is that lower forms of literature include realism and didacticism while the higher forms of literature create beauty through aestheticism.
In addition to explaining his philosophy, Poe dedicated most of "The Philosophy of Composition" to explaining just how he wrote "The Raven." Because "The Raven" was going to be a poem, Poe concluded that its purpose should be beauty. (This also applies to Poe's concept of "single effect.") It is then that Poe needed to decide upon the tone in order to achieve that beauty. This is the exact moment where your quotation appears:
Regarding, then, Beauty as my province, my next question referred to the tone of it's highest manifestation- and all experience has shown that this tone is one of sadness.
Here is where Poe's theory gets interesting in context because, next, Poe concludes that, because beauty always induces tears, the tone of his "beautiful" poem must be a sad and melancholy tone. (My response at this point is true beauty always induces tears, Poe? Really? However, "The Philosophy of Composition" is Poe's work, not mine.)
So, to answer your question in the most simple form, one could paraphrase your quotation as follows: Since beauty is my purpose and my goal, I had to ask myself how to achieve the best tone to exhibit this beauty. In my experience, the truest tone of beauty is a tone of sadness. Now, we might not agree with Poe here. (I don't. Not in the slightest.) But that doesn't take away from his point.
Poe goes further here and says that the absolute saddest and most melancholy subject of them all is death. Again, Poe concludes something interesting: when a death is beautiful, now THAT is a poetic subject!
The death, then, of a beautiful woman is, unquestionably, the most poetical topic in the world.
I wonder what Poe thought about the death of Hamlet's Ophelia? And in this way, Poe does a cannonball into poetic thought, snowballing from one idea to another. (Poems mean beauty; beauty invokes tears; tears mean sadness; sadness is the best tone; sadness will be the tone of my poem; death is the greatest sadness; if death is beautiful, "The Raven" will have quite a legacy.)