There are (at least in the U.S.) two meanings for the term "off-road". One of them is literal; Any time you are not on a road, you are "going off-road" or "off-roading". This is generally best done in a vehicle with four wheel drive/all wheel drive, with lots of ground clearance, and a strong suspension. Lots of people spend a lot of money enhancing pickup trucks, jeeps, and other vehicles for maximum ability off-road. Some people also consider a dirt road to be off-road.
The other sense is "not on a public thoroughfare", IE "on private property". Many automotive products are sold "for off-road use only", generally meaning that it is actually illegal to drive on streets while they are installed on your car. This is generally used as a disclaimer to avoid litigation if someone should get pulled over for them (or ticketed for them after being pulled over for something else.) Many items are for off-road use only in California, Washington, and other states with restrictive anti-smog laws, but perfectly legal in other places; check state and local statutes for more information.