Good question, John - escaped me for years as a homemade "grill master!"
Here's basically what happens: With large cuts of meat (and even thick-cut steaks), the juices in the meat (rendering fat and connective tissue) flow toward the surface of the meat during cooking. Also, the surface pores of the meat are wide open, allowing that juice to flow freely. If you remove a brisket, or pork butt (or even a steak) directly from the heat and cut it, that flow continues. This robs the meat of the juicy tenderness it could have. While yes, the meat juice on the plate it good to sop, it's even better still inside the meat!
Resting, as we use the term here, does not mean cold or cool meat! If done properly, you will barely be able to handle it with bare hands when serving! During the rest, we want to retain the heat, and reverse the flow of juices in the meat. The surface pores close, and the juice gets re-absorbed into the muscle tissue.
When you remove a large cut from the smoker, immediately double-wrap in heavy-duty foil. Then, place a towel in the bottom of a portable cooler, then the meat, then another towel on top. Close the lid, and let your brisket or butt rest! The meat can actually stay there for several hours, with barely any temperature loss. You will see a big difference in the amount of juice on the plate, or cutting board, after the rest, vs. just out of the smoker! The meat will be more tender, and much more juicy.
This is the "rest" in a nutshell, as I understand it in theory, and practice! I cover steaks, fresh off the grill, with one layer of foil for 5 minutes before serving. Still plenty hot, and so much more juicy!