Resting might refer to "reposo", the time after drying the parchment coffee, when it is held for 30-60 days to stabilize. In Brazil, the reposo time is longer. This step is critical for longevity of the coffee and occurs before processing/removal of the parchment. Coffee that is not rested in this way will fade quickly, becoming baggy.
Resting might also refer to the step after home roasting a batch; coffee brewed immediately has so much C0-2 coming off it that it prevents good extraction or infusion of water. Also, certain characteristics are not developed immediately after roasting, such as body. A rest of 12-24 hours is recommended, or up to 3-5 days for some espresso coffees.