There are many different methods that end in the polished edge...in most cases, these methods remove little-to-no actual metal and the purpose of it is to provide that finishing razor hone in which the edge aligned ideally...most sharpening in and of itself does not accomplish this, and this end polishing can fix some of the natural deformation that comes with the actual sharpening. The real world outcome is a edge that cuts with less effort and by realigning bent/stubble metal, it can actually prolong sharpness/usefulness of the edge.
Methods that can result in the polished edge can include polishing tapes, stropping, stropping with a paste, steeling, buffing, using a rotary device with a polishing backing and possibly paste, hand polishing, ultra-ultra-fine ceramics (as noted above the 1000 grit and often much higher, which most standard kits have nothing near this fine), among others. As my knowledge of sharpening is limited, chances are there are many other ways to do this.
The steel itself affects polishing potential as well. For example, D2 is not a very good polishing steel at all...it's a pain to do and the ultimate outcome is usually not as good as many other steels. On the contrary, Bohler's M390 MicroClean is one of the best polishing steels and despite its supersteel performance it is very easy to achieve a high-polish on (on my EP, it starts to polish and reflect even at only 600 grit which most steels do not, and by 1000 grit it's a very reflective polish. Once you do the polishing tape, it looks like liquid chrome!) M390 polishes so easily that I would not be that surprised if the stopping motions on a pair of blue jeans or piece of cardboard cause the edge to begin to shine! Benchmade uses both of the above mentioned steels, hence the reference to them.