This poem is titled "Delight in Disorder," and the speaker lays out exactly what kind of "delight" and "disorder" he means in the first two lines. He's not talking about the disorder of a messy room, but of clothing—and he finds "disorder in the dress" not frumpy or slovenly, but "sweet."
Why should disorderly dressing be so sweet, such a "delight"? Because it "Kindles in clothes a wantonness." In other words, it gives clothes a feeling of playfulness, naughtiness—and sexual promiscuity. The word "kindles" even suggests that disorder lights clothing up like a fire, making them smolder with passion.
This will be a poem about how imperfect, rumpled clothes suggest that their wearer has been having a lot of fun—and how the speaker finds the suggestion of that fun much sexier than a perfect, pristine exterior. In fact, the pleasure he takes from disorderly clothes is also about his delight in another kind of disorder: a wild sexual freedom that breaks out of 17th-century moral strictures.
The speaker's language already sets the tone of this more-than-a-little-lustful poem. Listen to the repeated sounds in this first couplet:
A sweet disorder in the dress
Kindles in clothes a wantonness.
Here, alliterative /d/ and /k/ sounds gives the poem a sing-songy bounce. That bounce fits in with the poem's couplet-driven rhyme scheme (here, "dress" rhymes with "wantonness") and with its pulse-like iambic tetrameter (that is, lines of four iambs, metrical feet that follow a da-DUM syllable pattern). The sexy whisper of sibilant /s/ sounds and the delicious liquid consonance of /l/ and /z/ sounds only strengthens that sultry tone.
Take another look at how the meter works here. While the first line is in perfect iambic tetrameter, the second does something a little different:
A sweet | disor- | der in | the dress
Kindles | in clothes | a wan- | tonness.
The first foot of line 2 is called a trochee (a foot that goes DUM-da), and this gives the line some extra galloping energy. It also matches the poem's themes: that deviation from the poem's main meter is, like the clothes it describes, a little messy!