A torus is a surface shaped like a donut. Imagine that I've painted two rings on a torus. One is on the outer surface, and goes through the hole in the center, coming around from the other side. The other ring is on the inner surface, and goes all the way around the hole in the center. These two rings of paint are linked.
I then cut a small hole in the torus. Through this hole, I turn the torus inside-out.
In the process, the rings of paint switch from the outer surface to the inner surface and vice versa. Therefore, they have become unlinked. How?
Charlie is correct with his second solution, I feel that he deduced the answer rather than solved it. I don't mean to take anything away from you Charlie, the conceptual leap required is by no means a small one.
In proving this, I feel the real challenge here is to visualise how to turn a torus inside-out. I post a description next....(But I really recommend you try it yourself first)