My mistress' eyes are nothing like the sun (line 1)
We start out talking about appearance right away. This whole poem is about beauty – the things we find attractive and the stereotypes we have about what women should look like. In this line the speaker starts out talking about his lover's eyes, and we expect him to give her a compliment, because that's what we've heard in a million different poems and songs. Instead, he switches it up on us, telling us that her "eyes are nothing like the sun." At first, it may be a little hard to figure out what this means. The comparison of eyes to the sun is a bit odd. Still, as we keep reading, we figure the speaker's strategy out pretty quickly.
Coral is far more red than her lips' red; (line 2)
The game here is to pick a clichéd image from a love poem and then blow it up. Someone writing a normal love sonnet might say, "My lover's lips are as red as coral." Shakespeare says, "No way!" He refuses this unrealistic comparison, choosing instead to ground his love in a truthful (and even somewhat harsh) assessment of what his mistress really looks like.
If hairs be wires, black wires grow on her head. (line 4)
Again, if you wanted to compliment someone on his or her hair, you probably wouldn't say, "Oh baby, your hair looks super wiry today." This makes his mistress sound like she just stuck a fork in an outlet. The point is the same as in the earlier lines. The speaker refuses to lie about his mistress's beauty. At the same time, he's starting to tell us something specific about the way this woman looks. We just learned that she has darkish (dun) skin (line 3). Now we find out that her hair is black. Not only are these not the most standard features for a fantasy woman in Western poetry, but they also give us the sense that our speaker is imagining a specific woman.