Most states have recognized that low-level offenses, particularly those committed by first-time offenders, shouldn’t necessarily trigger the normal criminal-case process. They’ve acknowledged that offenders with minor crimes may not be best served going through the regular court process of a plea and sentence or, in the case of a not-guilty plea, a trial. Counseling, rather than punishment, can often help and deter such people. (For information on a related topic, see Substance Abuse Treatment for Defendants Facing Drug and Other Charges.)
A "first offender" program is a way for a defendant to avoid the full effects of a criminal prosecution. It’s a type of diversion, often for those who have no previous criminal record, or at least no felony convictions.