The cushions and pillows of a new couch will inevitably be a bit stiffer than the ones you are replacing. The stiff cushions can make the simple act of relaxing on the couch a bit of a pain, literally. While the cushions will naturally break in over time, there are few ways you can hasten the softening process, depending on the material and urgency.
Sit on it. If you recently bought a new couch, the cushions will certainly need breaking in. Give it time. Through daily use, the stuffing will soften, making it more comfortable.
Remove some of the stuffing. Most cushions and pillows will have a zipper along one of the seams. Locate the zipper and remove some of the stuffing. Depending on the filling, this may not always be feasible (such as with foam filling).
Have the cushions restuffed. Take the firm cushions to an upholster who can remove and replace the cushion filling to your liking.