When seated on the saddle, your weight is primarily supported (or should be) at the ischial tuberosities which are commonly known as the "sit bones".
Quoted from Wikipedia:
When sitting, the weight is frequently placed upon the ischial tuberosity. The gluteus maximus covers it in the upright posture, but leaves it free in the seated position.
Essentially, there is very little sub-cutaneous fat or muscle tissue covering the sit bones while sitting on a bicycle saddle and thus little "padding" between the skin and bone. So, when you go through periods of not riding or are new to riding, that region is not adapted to compression and impact from the saddle. After riding for a while, the bone, tendons, and muscle in that region adapts by strengthening in that region, and no doubt vascular and nerve changes occur as well.
What happens in the case of an inexperienced cyclist or one getting back into cycling, is that micro-damage occurs to the bone, muscle, tendons and other tissue in the area. The micro-damage leads to inflammation and thus pain/soreness. At that point, the the tissues begin to repair and strengthen. The bone is thicker and stronger, the muscles/tendons are stronger, nerves are adapted to the stresses, new blood vessels, etc. Once those tissues have remodeled and healed, there is no more soreness. (Actually, the process can happen again if one goes say, riding for 3 hours to riding for 6 hours, but usually won't be as bad the second time around.)
It's pretty much like any other area of the body that goes through the adaptations from not being exercised to being exercised. So, one gets sore at first, but as muscle/skeletal tissue adapts, one is not sore later on. To some degree, the issue is similar a bruise, but it's much more like the muscular/skeletal adaptations that occurs from exercise.