At the moment when a roast is removed from the oven, the meat near the surface contains fewer juices than the meat at the core. This disparity occurs because many of the juices that were originally in the outer meat either evaporated or were forced towards the center.
If you carve a roast immediately after cooking, when its juices are unevenly distributed, the edges of your slices will be unnecessarily dry. In addition, many of the meat's juices will seep out because the saturated muscle tissue in the interiror cannot absorb and hold all the excess liquid that has collected there during cooking.
A 15 to 25 minutes respite (depending on the roast's thickness) gives much of the liquid a chance to redistribute and settle throughout the meat. This brief rest also allows the meat to become a little firmer, making it easier to carve thin slices.