Consider the two rings that this magician is holding in his hands:
How would you describe that configuration in topological terms?
From a knot-theory standpoint, I would say that the rings form a two-component link that is equivalent to a Hopf link. I'm no knot-theory specialist, though; they're may be a simpler way of putting it.
I'm wondering what technical term is used in topology to describe that type of relationship between such a pair of sets.
"Two (solid, unknotted) tori embedded in $\Bbb R^3$ are linked iff their complement has abelian fundamental group" works. You need to mention the ambient space in some way because without it they're just two separate tori with no relationship with eachother.
New attempt:
If we have one ring $R$, then the other ring is linked with it if it not continuously deformable to a point within $\Bbb R^3\setminus R$. (In this case it's easier if the rings are thought of as circles, rather than tori.)