This is a bit of a "layman's" answer but here goes:
Space, not just the world we all live in, but all the space in the universe is "affected" by MASS (massive objects) in a way that most people do not realize. Most people think that gravity has something to do with a "magnetic" force of some kind that causes objects to be attracted to other objects. The weird truth of it is that "gravity" is a side-effect of the "geometry" of space-time.
What does that mean? What Einstein figured out is that SPACE is actually "warped" or "curved" by mass (or massive objects) like the Sun or planets, or black holes - that sort of thing. Now while you cannot really SEE this,
you can see the "effect" of it. When an asteroid passes closely by a massive object, it may be affected by the objects gravity and drawn toward it. But this has nothing to do with magnetism - it is actually the effect of the asteroid following the "curvature of space" (since the massive object - like the Sun - has warped space).
To think of a common, simple example: imagine a BOWLING BALL sitting on a large rubber sheet (or your mattress).... you will notice that the massive ball makes an big depression in the sheet, or "dip" in your mattress. Now imagine rolling a marble across this sheet, or your mattress. If it is close enough to the bowling ball, it will be "captured by the gravity" (really warped space) and spiral inward toward the bowling ball. So "Curved Space" is the "warping of space" caused by "massive objects", and what we see as gravity is really just objects responding to the natural curvature of space.
Many people then ask why an apple falls straight to the ground on earth. The general idea is that space is "more steeply curved" when close to massive objects (as we are standing on earth) and since we are already ALWAYS in motion (you knew that - with rotation and all), when you "let go" of a ball, it follows the path of least resistance in curved space, which is right DOWN to the ground (now that is a "steep curve").
-Gregory J. Mallon, La Plata, MD
From reading multiple books on relativity and space (space-time). recommended: Timothy Ferris' book: "The Whole Shebang" (a great chapter on curved space)