Carlyle:
Floating refers to a construction process/technique where normally a small piece of construction equipment such as a "Sand Pro" or simply a small tractor is used along with a variation of float boards, boxes, blades...they have many names, and dragged behind the equipment and driven across the surface of the green in a specific manner (with the contour, not against it) to blend/create the surface character/contour desired by the architect/shaper.
You can imagine a green that has been stripped of its sod and as Tom says, the top 2-3 inches of topdressing as well, or a new green being constructed, where it has been filled to grade with sand and roughly compacted and now the sand SURFACE needs to be floated, smoothed out if you will, to achieve the desired final grade.
Hope this helps.