Resting allows the juices in the meat to redistribute so that they will not gush out when you cut it (ending up with a dry piece of meat). I think the minimum for resting is an hour. Putting it in the cooler is just what it says. You put the meat in a cooler which will help keep the meat warm while it is resting. Some will put it in an oven which effectively does the same thing. No ice. You can wrap the meat in towels, butcher paper, or foil.
Chargriller with SFB, Master Forge Vertical Smoker