She walks in beauty (line 1)
This is a funny way of describing someone – what does it mean to "walk in beauty," anyway? Is "beauty" some kind of cloud or vapor that the woman is walking in? Or is it like a comfortable pair of shoes?
And all that's best of dark and bright Meet in her aspect and her eyes: (lines 3-4)
This woman's beauty takes the "best" things from both ends of the spectrum ("dark" and "bright"). And it's not just that she has a pretty face – her whole "aspect," or appearance, is harmonious and lovely.
Thus mellow'd to that tender light Which heaven to gaudy day denies. (lines 5-6)
The balance of "dark" and "bright" in the woman's appearance sort of averages out into a "tender light." It's like she casts off a glow, but a soft one, or something.