it's not clear what context the term is being used. You might see a question such as "have you ever been convicted of a criminal non-traffic offense?" Used in this manner, it is a broad category which includes any offense that is not a traffic offense. This would include everything from the most basic misdemeanor to the most serious felony crime.
To answer a little bit more specifically then the first attorney, specific examples of such types of crimes are assaults, no contact orders violations, possession of drugs, thefts, etc. I hope this is what you were looking for.
To best answer your question, I will describe what a criminal traffic offense is. A criminal traffic offense is any crime involving a motor vehicle, like DUI, reckless driving, negligent driving in the first degree, vehicular assault, vehicular homicide, and hit and run (attended and unattended).
A non-traffic criminal offense is all other crimes (not infractions). Examples include: assault, disorderly conduct, theft, possession of marijuana and other drugs, murder, arson, malicious mischief, among many, many others.
DUI Marijuana DUI Criminal defense Crime classifications Felony crime Misdemeanor crime Crimes against society Criminal charges for disorderly conduct Possession of a controlled substance Marijuana laws and criminal charges Crimes against property Criminal charges for arson Criminal charges for theft Criminal charges for assault and battery Homicide Criminal charges for murder Violent crime