To put it simply, the theme is that "beauty is in the eye of the beholder" and/or, perhaps, "love is blind."
The sonnet appears below, and my analysis in brackets underneath lines as necessary:
My mistress' eyes are nothing like the sun;
(Favored eyes as far as beauty goes, tend to be bright. Her's are dim.)
Coral is far more red, than her lips red:
(Red lips were the fashion, and indicate health, but hers are pale like coral.)
If snow be white, why then her breasts are dun;
(Albaster white skin was favored in Shakespeare's day, but hers is yellowish. He chooses her breasts in particular to which to make this unflattering comment, further reducing her appeal as a woman.)
If hairs be wires, black wires grow on her head.
(Yuck! The image conjures the mythical Medusa, not known for her feminine wiles...).
I have seen roses damasked, red and white,
But no such roses see I in her cheeks;
(Rosy cheeks indicated youth and beauty; she has none at all.)
And in some perfumes is there more delight
Than in the breath that from my mistress reeks.
(Bad breath too. Oh my.)
I love to hear her speak, yet well I know
That music hath a far more pleasing sound:
I grant I never saw a goddess go,
My mistress, when she walks, treads on the ground:
(He does not romanticize or idolize his lover.)
And yet by heaven, I think my love as rare,
As any she belied with false compare.
(The clincher: Despite all of her physical shortcomings, to the speaker, his lover is better than anyone he could compare her too. He loves her.)