While the BBC allude to the description in the Applied Physics Letters, the huffingtonpost.com cite it and provide their own layman's summation...
The prototype flying carpet is described in the journal Applied Physics Letters: "We use integrated piezoelectric actuators and sensors to demonstrate the propulsive force produced by controllable transverse traveling waves in a thin plastic sheet suspended in air above a flat surface, thus confirming the physical basis for a 'flying' carpet near a horizontal surface. Experiments are conducted to determine the dependence of the force on the height above the ground and the amplitude of the traveling wave, which qualitatively confirm previous theoretical predictions."
In plain English, "We've created a flying carpet! Don't stand on it yet please, you'll break it. Give it a few years -- or decades."
