Poets use poetic techniques such as similes, metaphors and alliteration to increase the depth, profundity, mood and tone of the piece. Let's take a look at the first stanza that you have mentioned, and see how those devices have an impact. The very first line contains a simile (comparing two things using "like" or "as"): "She walks in beauty like the night". Byron then goes on to expand on that simile, saying, that like the night, her eyes have "all that's best of dark and bright", referring to the beauty of the dark skies, and the light of the stars. Using a simile here greatly increases the depth of what Byron is saying. He could've just said, "She sure is pretty" but instead compares her beauty to the vast and eternal sky; that says so much more.
The alliteration in the first stanza adds a serene, rhythmic feel to the poem. Using "cloudless climes" and "starry skies" gives the poem a soothing, melodic, lyrical quality to the poem, increasing its beauty. Both of these techniques enhance the impact, the beauty and efficacy of the poem.