chkdsk.exe is a tool I use quite effectively as a sys admin.  However
I do not understand what is going on "under the hood" and usually
returns fatal blue-screas back to working computers.  What exactly
does chkdsk.exe do to the hard drive?

Hi, 

CHKDSK has a number of functions. At it's most basic level it checks
filesystem integrity and performs repairs if requested. It can also
scan for physical drive errors.

The Windows file system is basically a big database that points
filenames to specific data on the drive. It is this database that
CHKDSK is working with, to ensure all the data it is pointing at is
correct, and that all data on the drive has files pointed at it.

When your computer is shutdown incorrectly or file write operations
are interupted for some reason, it is possible for Windows to 'lose'
files. The data exists on the hard drive, but it is not visible as a
file. Also in some cases files can be deleted, but the space on the
hard drive is not freed up. CHKDSK's repair functionality scans for
these sorts of errors and corrects them where possible.

When using CHKDSK's /f option, it gives you the option to move any
lost data that can't be relocated into files. It creates files called
file####.chk (where #### is a number) that can be examined. Sometimes
seemingly lost data can be recovered this way. Unfortunately it can be
difficult to identify the contents of binary files, which is when you
need an application to identify file type independant of file
extension, such as:
http://www.daubnet.com/english/identify.html 


Here are some references:
http://www.pegasus-afs.com/eSupport/using_CHKDSK.htm
http://en.wikipedia.org/wiki/CHKDSK
http://www.microsoft.com/resources/documentation/windows/xp/all/proddocs/en-us/chkdsk.mspx?mfr=true

(Old, in relation to MS-DOS CHKDSK, but still offers some useful information)
http://www.borrett.id.au/computing/art-1985-11-01.htm

I hope this helps, let me know if you need clarification.

Regards,
Sycophant

Simple yet informative answer.  Thank you very much.