A serious delinquency is a piece of negative information that will damage your credit. Most of the time, their origin is from a mistake caused by improper use of one's credit. The most common example of a serious delinquency would be a late payment.
Keep in mind though, each creditor/lender has their own interpretation of what constitutes a serious delinquency. Some of them might consider a 90-days late payment to be a serious delinquency, while others might wait only 30 days before reporting it as such.