Convertible top weatherstipping is the felt-like material that runs along the base of your convertible top and helps to provide a weather-tight seal. Actually made of a microsuede or fiber, this type of piping is applied to the bottom of your convertible top. When you snug it down with the electric motor, the windshield clamps the material, and “fills in” any gaps which may have been left before the roof is finally locked into place. Like standard door weather stripping, this is applied to the active member of the convertible roof, as it cannot work in any other fashion.
For more info, see How to Repair a Convertible Top