The article that mentioned "over-burr" is no longer on the web. A number of articles talk about "top burr" and "wire burr".
In this video, it is the sharpest part of a steel blade, the "apex", after the grinding process has pushed it over to one side, and possibly lengthened it. See the picture at the start of
http://player.mashpedia.com/player.php?ref=mashpedia&q=tiIsAn1ZGkwIn knife and razor sharpening, it is common to create such a burr, then switch sharpening sides, and grind on the opposite side, until the burr has moved to the opposite side, many, many times. This creates a very fine, well polished edge, that acts very, very sharp. E.g., see
http://devilsfoodkitchen.com/2016/04/01/101-knife-sharpening/The first video talks about removing the burr. But it looks to me like he "removes" it by the same process as he creates it - i.e., he moves to sharpening on the opposite side, but only long enough to take the burr to the top, but not to bend it over again.
Skate grinding also only sharpens and polishes on one side - the hollow side. Then you use the flat stone to polish the opposite side. If you want to genuinely deburr, you can do so by drawing the stone somewhat across the edge, say at a 30 - 45 degree angle relative to the side. This effectively cuts off the burr. E.g., that's what Mike Cunningham does, unless the skater requests otherwise, though at the final step he uses a hard rubber "stone" to do it instead of a grinding stone.
Here is an article about the wire edge
http://www3.telus.net/BrentBeach/Sharpen/wireedge.htmlwhich the author claims occurs when the the grinding process removes the crystal structure (a form of "tempering"), so that the steel is no longer hardened. But since he is talking about cutting tool use, he feels that such a soft edge is useless, and he wants to remove it.
Some skaters and skate techs feel that the burr, moved to the top (the bottom when you orient the skate for skating) is still useful in ice skating, because ice, at ice rink temperatures, ice is fairly soft. They (including myself) feel it is thin enough not to create much drag, but deep enough to create lateral resistance to skid, and makes it easier to push. OTOH, many speed skaters prefer to remove it, because they feel the drag is more important than the improved push. If you know any speed skaters, you know that they sometimes debate the advantages of each style.
OTOH, now that I sometimes work as a rink guard, and volunteer as a skating instructor, it wastes too much time to constantly take of and put on the skate guard, when I come on and off the ice, so I no longer want the blade that sharp. Supersharp edges are just too fragile for walking on the rubber mats, because they sometimes bend over and become worthless.