In addition to a more relaxed body geometry, "plush" can also refer to the ride "feel." Steel and carbon bikes, for example, are said to give a more comfy, plusher ride than aluminum or other materials. The Specialized Roubaix, which started it all, was originally developed for the "Hell of the North" Paris-Roubaix race over the cobblestones. As the field has developed, they are now making plush bikes that also go fast, although not as fast as the higher end race or pro style bikes.

Then again, as OakLeaf noted, you can also get a plushier ride by letting a little air out of the tires. A slower ride, but plushier!