Procedures vary from state to state; I could nitpick Uncommon Sense’s obviously fairly good summary of Wisconsin procedure on the basis of the different procedural methods used by New York and by North Carolina, but to what purpose? Unless someone familiar with the New Jersey traffic court system cares to handle that.
There’s one basic point that tends to get overlooked here, though, and that is that procedurally a traffic offense is criminal, not civil. That is, it’s not a lawsuit where the court adjudges whether you in fact owe Barney the $700 he claims for the lousy repair job he did in one afternoon, which fell apart three days later. It’s a situation where the state in its prosecutorial capacity alleges that you committed an offense, against which you may defend yourself. Hence, while traffic offenses are “barely off the grass” on a vertical scale of severity of offense, the same general rules apply as in a criminal trial, with a few exceptions (for example, if you can’t be sent to jail for a substantial period, you’re not entitled to a jury trial; if you were ticketed rather than arrested, Miranda safeguards don’t really come into play; etc.).
But the key point is that, presumably following standard procedure, the police officer (a) felt himself obliged to ticket you for Careless Driving, and (b) believed that your case was such that a reduction to a lesser charge was something you might be entitled to. Now, you have the option of pleading guilty by mail – which would cost you a fine and points – or to appear and essentially plea bargain. You do not need to plead guilty – though “going to trial” would consist of you entering a not guilty plea, the judge or the D.A. asking the police officer to tell what happened, you having a chance to explain why you’re not guilty, and then the judge finding you guilty (possibly not guilty, but Anna Nicole’s will didn’t leave you anything either, and one’s as likely as the other). However, if they can simplify this by reducing your charge to, say, “Failure to Keep Right” (always a fun choice) in exchange for your agreement to plead to it, that saves everyone time and heartache. Remember that your right to plead and the time and frustration of even a summary trial (described above) are weapons on your side, and you have room to negotiate.
(IANAL, and I am making general observations about how the law works in similar situations to the one you describe, not giving you legal advice, which I am not licensed to do and don’t know the facts of your case well enough to give valid and useful legal advice even if I were licensed. While you probably don’t need a lawyer for this, getting some specifics from someone who knows New Jersey traffic laws would be very useful for you.)