The fuel pump, AKA the 'HFCM' or horizontal fuel conditioning module is where your primary fuel filter goes into and gets riddled with crud some of which that ultimately passes through the fuel filtration system and into your injectors. Brake cleaner is the tool of choice to remove all the goo, though note that you'll want to pick up some quick disconnect tools to remove the module. You'll also need the bowl filter kit to put everything back together.
Note also that the brass drain plug that many 6.0's came with is SOFT. Be sure to insert your allen wrench COMPLETELY IN the module to remove the water/fuel as step one in the removal process.
A great video on the procedure can be found on YouTube, compliments of Bill Hewitt from Powerstrokehelp.com.
A writeup on the removal itself is on thedieselstop.com. If you DO end up damaging the plug, we offer a handy thumb screw version.