Are pressure sores serious?

Yes. Yes briefly there are 4 types of stage 1 through stage 4. Stage 1 is relatively superficial with intact skin, where as stage 4 is down to the bone. Once one has gotten one they are much more likely predisposed to having one again.
They can be. When they get deep, they can become so large that surgery to repair them can become less possible. In this case, wound care and a slow course of healing is the rule.