Hi 370,
Over here in Western Australia you can get off-road registration for a dirt bike or quad, which costs around $12-00 per year and is issued by the same place that does the road registration.
The state government has made a number of designated off-road recreation areas available, where you can your ride dirt bike or quad, without the need for a normal road license. You do however need to get this off-road registration, otherwise the ranger can confiscate your bike and issue a fine.
Once you pay the $12 they issue you with off-road plates, which you are required to display on your bike. This is so you can be identified if the ranger finds you lying dead next to your bike somewhere - don't laugh it happens!!
I don't know if any of the other states run this system - but maybe it's this type of dirt bike registration you've heard off.