If you manage to convince your students that smooth manifolds are among the most beautiful and interesting objects in mathematics, expecially dimensions 3 and 4 that model our universe, then you can say that (among other things) knots form a fundamental ingredient in understanding and constructing such models.
For instance, you can tell that by removing a (well-chosen) knot from $S^3$ we can get the simplest possible universe with a hyperbolic geometry having finite volume. Or that every 3-manifold may be constructed by removing and "regluing" (finitely many) knots.
