What does "peace comes dropping slow..." mean in "The Lake Isle of Innisfree"?

When the speaker notes that "peace comes dropping slow," he means that time unfolds at a measured, leisurely pace on the isle of Innisfree. He dreams of moving from his urban life standing on "pavements grey" (gray sidewalks), to the serenity of this rural isle, where all alone he will have his small cabin, his bees, and his nine rows of beans.

In the second stanza, he notes that peace will come from the measured rhythms of nature, to which he will align himself. He will find peace in the morning mist, the song of the cricket, the midnight starry sky, noon's "purple glow," and the insects that come out to fly in the evening.

This is a dream of a return to a paradise of simple living close to nature where existence is slow moving.

The speaker longs for the quiet solitude of nature.  Currently, the speaker lives in an urban setting (in the second to last line of the poem). He has been dreaming of going to such a place and being able to relax and enjoy his life, rather than scurry about like he does in his stressful city life.

This line just means that he will be able to relax and have peace.  This line gives action and/or power to the word "peace."  Normally, peace and powerful do not go together--but here it shows how important it is to have solitude.  If it comes "dropping slow," then it will be a long, drawn-out process and the peace will continue on for the speaker.  That is exactly what he wants.  He longs to get away from the hustle and bustle of city life and enjoy the everlasting peace that nature offers us.

Why does "peace [come] dropping slow" in "The Lake Isle of Innisfree"?

One doesn't normally associate peace and action—be it "dropping" or anything else. Yet in this case, the line "peace comes dropping slow" indicates that, for the speaker, peace is not simply an absence of noise but something positive in its own right. It's something that makes its presence felt, as if it were dropping in from above, like a rainstorm or a snowfall. But seeing as it's peace (and not some violent weather pattern we're dealing with here), it drops only slowly, descending upon the speaker ever so softly.

It is notable that the dropping peace experienced by the speaker comes from the "veils of the morning," when all is quiet, and all is calm and relaxed. This is just what the doctor ordered: a moment of relaxation for the speaker, far away from the hustle and bustle of urban life.