A clean driving record is one that is free of accidents, moving violations or points. An insurance company also likes a record that is free of claims.
What an insurance company, employer, etc, considers a bad driving record can vary. A simple speeding ticket for only a few miles over the limit may not affect your insurance or be a problem for some employers however others may want a driving record completely free of any type of moving violation or accident, no matter how minor.
Your relative would need to speak to the hiring manager of the job, or in the case of being a firefighter perhaps the training manage, to seek clarification on what exactly the company, either private or a government or state employer, determines "clean" to mean.
In general as a minimum a company will want 3 to 5 years without moving violations on the person's record, thus a clean record. Many employers though prefer or require 10 years with a clean driving record.
State laws differ regarding driving records and how long drivers, insurance companies and employers can request a copy of the record for but it appears that many employers can look back at your driving record for the past 10 years. Employers may differ on how long they look back though depending upon their internal guidelines.
If you want to find out if your state limits how far back an employer can check your driving record, check with your state's Department of Motor Vehicles. Since you live in Pennsylvania this would be PennDOT.
Your relative should thus check with whomever would be in charge of training or hiring firefighters about how long their "look back" period is and what they mean by a clean record before he gives up his dreams. He may also want to contact PennDOT to see if there are any want to get any of the items on his driving record expunged.