The woman's beauty is related to her movement from the beginning – part of what makes her beautiful is her dynamism and life. She's not just a portrait on a wall, she's a living, breathing, "walk[ing]" person.
Meet in her aspect and her eyes: (line 4)
So the woman's beauty has as much to do with her entire "aspect," or overall appearance and expression, as it does with any one feature. The whole package is lovely.
Which waves in every raven tress, (line 9)
The whole "aspect" might be gorgeous, but that doesn't mean the speaker doesn't want to linger admiringly over each individual feature. It's also important to remember that traditional, conventional standards of beauty at the time held that blondes were the pinnacle of hotness. So Byron's praise of a brunette here actually flouts traditional standards of beauty.
Or softly lightens o'er her face; (line 10)
Byron has said that the woman's whole "aspect" is beautiful, but now he's trying to put his finger on exactly what makes her facial expression so gorgeous.
And on that cheek, and o'er that brow, (line 13)
Now Byron's attempting to break down her beauty, one piece at a time, in order to understand it. It's like he's dissecting her beauty.
The smiles that win, the tints that glow, (line 15)
The woman's smiles are "win[ning]," and apparently she blushes a lot – is he trying to suggest that she's a bit of a flirt?