If you’re an Americanist archaeologist: Nothing.
He is clearly within an undifferentiated layer of yellowish sediment. He’s been digging in arbitrary levels and pedestalled a biface for recording its depth, then will collect the biface and level the pedestal to the arbitrary “floor” he has excavated to in the rest of the unit.
If you’re a British archaeologist: Everything.
He has clearly hit a surface that the biface used to sit on, and he should have levelled to that floor to preserve context, recorded everything on the surface, then removed the biface and continued until he found the next surface, as signalled by a stratigraphic change or more artifacts. By pedestalling the artifact he removes its context.
Nice biface, regardless!
(My thanks to Travis S. for posting such a graphic example of this.)
Colleen Morgan 
Actually, my first thoughts were (1) what a sloppy-ass pedestalling job and that sidewall looks none-too-vertical either; and (2) they really ought to have a dual English-and-metric scale in there.
But then, I’m a historical archaeologist (historical archaeologists do it in multiple measuring systems!)
There are merits to both. Much “Americanist” archaeology is done on short time frames and small budgets, so you certainly can’t go pedestaling every little flake and burned rock at a certain elevation just because you hit a nice biface/projectile point/insert neato artifact of your preference here. If you were to “excavate” and planmap the floor of my house, are you really going to note every cat hair just because there’s a few cat toys strewn about?
On the other hand, it leaves a lot of work for the analysis stage and a lot of important information can only really be rendered as bulk data (often in mere tabular form).
Lastly, by following the second method, you are still creating an arbitrary level defined by the position of something whose value is being assigned by the modern excavator/interpreter. Also, it’s assigning a cultural significance to the position, which could just as easily be due to natural transformations.
It sure is a nice biface, though!!!!!
Sara – I used to pride myself on my pedestals, until I came to see them as somewhat methodologically unsound. And when I had to pedestal a whole bunch of stuff early last summer that I was fairly certain was sitting on a floor. bah.
Regardless, it was fun learning to think of things in Spanish varas at the Presidio.
John – I think the argument more would be that you wouldn’t pedestal anything, but would excavate it to try to determine if there is a living surface that it is sitting on.
I would agree, to a certain extent, with your second point. Especially in that homogenous silt.
Unless you’re working in the Mojave Desert. Then all bets are off…
Thanks for the comments on the pic.
Actually, if you care to know about the context, there was no living surface, it was a solitary find. Therefore, there was no other context to associate with the biface, so it was left pedestaled as the floor was excavated. As was speculated, this was dug at arbitrary layers, but would you really suggest that it be dug by natural layers that might be half a meter deep? That seems a little silly to me. Maybe you should do the research and try to get some context on what is being criticized.
As for Sara: (1) What difference does the aesthetics of a pedestal make when it’s an amateur photo? (2) Metrics is a much easier unit of measurement, so as this was a prehistoric site, why should we bother with English methods? I suppose it would be easy for you to keep walls perfectly straight as you only have to go a foot or so down. Our excavations go as deep as 2.5 meters as we are going back 10 – 12 kya.
I meant no offense in linking to your picture, and I am sorry that you have taken it as such. I dug (and still dig) in the American style, and I have spent many hours trying to explain to Brits why we dig in arbitrary layers in America (the undifferentiated yellowish sediment), and I felt that your photo might explain things to them a bit better.
It’s OK. I suppose the difference might be that defined layers might be easier to come by in a more compacted sense over in the UK, as opposed to Alaska that may go for thousands of years without anybody making a distinct settlement in an area.
I suppose I shouldn’t make too much of a stink about somebody appreciating my picture, but I think I took the most offense from Sara’s comment more than anything–picking on a first-time field student. Since when was pedestaling a science?! The provenience measurements are still the same no matter how it looks.