>>125502434-dimensional manifolds in general are a bit difficult to envision, but you can usually use lower-dimensional manifolds as an analogy. For example, the curved surface on an infinitely long cylinder is a 2-dimensional manifold. "Straight" lines on such an object spiral around the cylinder forever in a helix, which is kind of like circular motion if you consider the cylinder's long axis to be the time axis.
It's important to keep in mind that the curved manifold you should be envisioning is spacetime, not space. an orbiting object never loops back on itself in spacetime, because it's always moving forward in the time dimension. in this sense, the term "orbit" is maybe a little bit misleading at first, intuitively.
if you're not studying the actual subject, I 'm not sure there's very much insight you get from thinking in this way, but one thing that makes a lot more sense is the feeling of weightlessness when you're falling. you don't feel any forces on your body because there are none. It's a lot simpler of an explanation than the gravity-as-a-force explanation of the same feeling.
