BU, Brilliant Uncirculated. Uncirculated coin with the look that it came out of the mint yesterday. Still shiny but not polished. Not officially a grade like Uncirculated, but BU is a little better for a collector who can afford it. Matter of personal taste for the collector realy.
I should have chosen "Cut-n-Paste" as a forum name, since that is what I do, mostly.
UNC and BU are also terms that are fading away and being replaced by a newer, more complicated system. TPG's(Third Party Grading Services), coin dealers and collectors alike are swinging into a system where MS(Mint State) is replacing the UNC and BU system. With the MS system there are now numbers added to the MS to differenciate the conditions of coins. You may still see UNC and BU used by older people that just don't like the new system though. Me occationally. So when you see things like MS62, MS66, etc. those are the new notations that basically mean UNC or BU.