Intuitively, just imagine picking a starting point on each of the circle and the knot. Now walk at different speeds such that you get back to the starting point at the same time.
In fact, that's what the knot is: a continuous, bijective mapping from the circle to the image of the mapping, i.e., the knot. (As the linked answer says.)
Edit: I see now that the article already has this intuitive explanation but with ants.
Somewhat counterintuitively, all knots are homeomorphic to each other.
If you regard two spaces being homeomorphic as meaning — roughly — that if you lived in either space you’d not notice a difference, it makes sense. To a one-dimensional being (that has no concept of curvature or length, since we’re talking about topology here), they’d all feel like living in a circle.
Only because "homeomorphic" is a highly technical term that most people don't even know the definition of, let alone have an intuition for, and because "knot" in math is a closed loop, unlikely "knot" in common language.
Once you know the definitions and have learned to tie your shoes, it's quite intuitive. Even a small child can easily constructively prove that knots are homeomorphic.
Homeomorphic is also interesting because it's a very fancy sounding word for a concept that has very few requirements to be met. It's usually a basic requirement for concepts in topology, but it does very little to distinguish topological spaces. It's essentially a highfalutin word for "these things are basically the same thing in a very basic way".