Wanderers in that happy valley, Through two luminous windows, saw
These lines start a new stanza, and a new description of the lovely palace. The speaker tells us that, when "wanderers" (notice the emphasis on aimless relaxation) passed through the "happy valley," they could see through two "luminous" (that just means full of light) windows in the palace.
We don't know what they could see, because Poe is saving that for the next line. Breaking up the meaning of a sentence over several poetic lines is called enjambment, and in a case like this it helps to pull us along through the poem. (Go hit up "Form and Meter" for more on that technique.)
Why just two windows? Well, we can't quite tell what that's about yet, but let's just keep an eye on these odd details.
Spirits moving musically, To a lute's well-tuned law,
The wanderers see "spirits" through the window, "moving musically" (alliteration alert!) around the palace.
The music they are moving to comes from a lute, which is an old-fashioned stringed instrument, a little like a guitar. The "law" of the lute is its rhythm, which regulates the way the spirits move. The basic idea here is that everything is in harmony. This palace is in good shape, inside and out.
Round about a throne where, sitting (Porphyrogene!)
The spirits are moving around a throne, where someone is sitting. We don't know who exactly, yet, but Poe gives us a (kind of dorky) little hint with that single, weird-looking word in line 22.
In case you're wondering why you've never seen this word before, it's because Poe made it up.
What does it mean? Glad you asked! It's derived from another $500 SAT vocabulary word, "porphyrogenite," which literally means "born to (or in) the purple." Hmmm… that's probably not much help, is it? Well, purple was a color associated with royalty in ancient Constantinople, and so someone born to the purple was a member of the royal family.
So, when all is said and done "Porphyrogene" means something like "royal" or "born a king." It seems safe to assume that it's the king sitting on that throne that the spirits are dancing around.
In state his glory well-befitting, The ruler of the realm was seen.
It turns out that it is the king, the "ruler of the realm" sitting on that throne. He sits in "state," which in this case means opulent or magnificent surroundings, the kind of beautiful that would be suitable "well-befitting" for a king.
Just who is this ruler? Well, we learned in line 5 that the ruler of this kingdom is "Thought." What does that mean, though?
Well, it's part of the riddle at the heart of this poem. Let's see if we can decode it…