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.