Suppose I told you that putting on a seatbelt makes you drive more dangerously.
"Nonsense!," you might think, "why would wearing a seatbelt change how I drive?"
Well, suppose I told you instead about a different car modification: a very sharp spike that attaches to the front of the steering wheel, so that if you brake suddenly you'll fly into the spike. What would that do to your driving? I think we can all agree that, somehow, you would find a way to drive even more carefully and safely than usual. Because you know how bad things would be if you got in an accident when you have a spike on your steering wheel, you will be extra careful not to get in an accident in the first place.
But if the spike makes us drive extra carefully then another way of saying the same thing is that not having a spike makes us drive more dangerously. Whenever the car gets safer (e.g. by removing the crazy spike on the steering wheel), our driving becomes a little less careful as a result. We might not purposefully drive recklessly, we just won't necessarily go to the same extremes of effort to be as slow and careful as possible.
You can see where this is going. Putting on a seatbelt – like removing a spike on the steering wheel – makes your car a little bit safer. As a result, putting on a seatbelt (like taking away a steering wheel spike) will make us drive a little more dangerously.
Now, of course there's a big difference between a spike on your steering wheel and a seatbelt: the spike can only possibly do you harm, whereas the seatbelt makes you safer in case of a crash. But the point is that things like seatbelts won't make us quite as much safer as you'd think because of offsetting behavior: the extra safety from the seatbelt causes us to drive a little more dangerously, which offsets some of the safety gains from the belts.
Further Reading: the blog Offsetting Behaviour has the Steering Wheel Spike as its banner image, and the full story of how the spike example came to be used to explain this concept. Check it out!