From the instruction manual: "When an external field is applied to a material, the magnetic moments produced by the tiny current loops caused by the orbital motion of electrons tend to align themselves in such a way as to oppose the applied magnetic field (Lenz's Law). [All materials are inherently diamagnetic, but] materials in which this is the only response are called diamagnetic." In a language a little closer to English: the little piece floats above the powerful magnets because the magnetic field from those magnets evokes an opposite response within the little float-y piece, which creates a current, which the magnetic field of the magnets can act upon by F = IL x B, creating an upward-pointing net force, causing the little float-y piece to float.
Here are the pieces separate. Note: actual size is far, far smaller than this.
Here they are together. If you are viewing this on your phone, the image is likely still larger than the actual pieces.
Side view!
