PBJ is also slang for "Probation Before Judgment". It's one of the many possible outcomes of someone going to court.
This term is mostly used in reference to the traffic courts of various states, but I have seen it for criminal offenses, as well. I have lived in Maryland for most of my life, and I have dealt with PBJ several times. Your mileage may vary with other states, but here's the gist of it:
A PBJ is usually given when there is enough evidence to convict you of a crime, but a guilty verdict is not put on your record. Instead, you are put on a probationary period where you have to not get in trouble again. If you do get in trouble, you will probably be punished for both violations (the old one as well as the new), so don't get in trouble! But if you stay away from John Law for the probationary period, the case gets dropped and you get away scot-free.
The beauty of it is that if this is given in traffic court, the judge will most likely reduce your points on your license and cut your fine in half (Maryland uses a point system, once you get a certain number of points in a two-year period, your license can be revoked... and insurance companies like to hike up the rates on drivers with points on their license). This means you pay a small fine, and there are no convictions on your record.
How long does the probationary period last? The judge will usually set it at six months or one year for traffic crimes, and up to three years for serious offenses. I've also heard that in traffic court, if a time is not set, then your period ends when you pay the fine, which is usually two minutes after you leave the courtroom. Sweet.