Reprofiling is redoing the primary edge bevel. Most edges have a primary edge bevel (thin angle) and a secondary edge bevel which does the actual cutting (wider than the primary bevel). Some knives have only one bevel. In a zero bevel flat ground blade, there is only one bevel from the edge all the way to the spine of the knife. A full flat ground blade with a convex edge has only the primary edge bevel, and the cutting edge bevel is actually convex, or rounded. Most knives have a primary edge bevel, and a very small secondary edge bevel.
Reprofiling a blade means to make changes to these parameters. Since this often requires removal of large amounts of metal compared to honing (making the cutting edge), the use of coarse stones is recommended to speed up the process.
Some knives (e.g. Benchmades) come from the factory with what some of us think are ridiculously wide primary edge bevels. Sometimes these are not of even thickness along the blade, or are set at different angles on either side of the blade.
Reprofiling simply means using coarse stones to adjust or construct this primary edge bevel. Usually, this means making it thinner and symmetrical on either side of the blade. The cutting edge bevel (secondary) is sharpened with finer and finer grits of stones after 'setting' the primary edge bevel.
Some people use these terms differently than the way I just did. It is important to define exactly which bevel (angle) you are talking about. In Joe's article, he refers to the blade grind as the primary bevel. I just ignore the blade grind altogether. It is hard to call a hollow ground shape a bevel.
So the primary edge bevel (to me) is that narrow strip that you can see along the edge of any blade. The secondary bevel is not necessary, but something I apply with very fine stones in order to strengthen the edge a little without compromising performance. You will probably not be able to see the secondary bevel with the naked eye. I hope this makes sense to you.
For additional help on understanding edge geometry and sharpening, see Joe Talmadge's excellent articles in the knowledge base section of BFC:
Edge Geometry
Sharpening FAQ
Paracelsus
[This message has been edited by Paracelsus (edited 09-15-2000).]