The speaker looks at "many hands" and sees something like a dance in them. It's a quiet, observant moment: hands at work, moving together, doing things that are "of great use" but cause "small trouble." That phrase suggests a kind of ideal labor, helpful and easy, without much fuss.
The last three lines set out pairs and contrasts: "dark and light," then "ice" and "wine." They read like a list of what those hands might handle or what a life contains, from cold and hard to warm and celebratory. The poem doesn't explain how they connect, so the reader has to fill the gap.
The title, "Begin the beguine," points to a dance, which fits the image of hands moving in rhythm. The mood is light, appreciative and a little mysterious. The speaker seems to find beauty in ordinary human activity, and the short lines give the poem a gentle, unhurried pace, like a few steps in a dance before it stops.