hi, brandon -
wrapping the beef in foil will allow it to continue cooking wihotut losing moisture. in effect, it braises the meat and allows it to become fall-apart tender. this can be over-done and if that happens you end up with mush, but the good news is that it's pretty hard to over-do it. just wrap it up and put back over the heat (you can use your smoker or an oven at 225-250 degrees) and continue cooking until the internal temperature reaches the desired mark. usually 180 for slicing, 190-200 for pulling, +/- a few degrees. this takes some time, but that is exactly what barbecue is all about, because the time and the heat work together to break down and render the fat, connective tissues and other "tough stuff" leaving thender, juicy goodness. this can be done without foiling, but some simply prefer to do it. my recommendation is to try it both ways and see which one you prefer.
as for the cooler, this is something that is a seperate operation and is done once the meat has reached the desired temperature. what you do is wrap it well in foil (heavy duty or a couple of layers of the standard stuff) or if it is already wrapped, then take it off the fire, and then wrap towels around that (this is to insulate the heat inside) and put it in an empty cooler. it should be there for at leat a half/hour, but can stay there as long as the internal temperature stays above 140. many times, pork shoulder and briskets are still piping hot after several hours in the cooler.
why is this done? there are a lot of reasons. the primary reason is to let the meat rest after cooking and let all the juices draw back into the meat and distribute throughout. if you cut open a big hunt of meat straight off the fire it's going to dump out all of its juces and in the case of a pork shoulder will turn an ugly brown on top of that. another reason is that meat keeps cooking a while after being taken from the heat and this resting time adds to the tenderness and flavor as any final collagen is melted down. a third reason is because your meat might be done earlier than you plan to eat (say it's done at 4pm and you want to eat at 5) or if you are doing several things on the smoker and some get done before others. this will help hold the meat until everything is done and/or everyone is ready to eat.
fridges are for leftovers, and they taste great the next day!
hope this helps.