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.