From what this layman can comprehend of Einstein's relativity is that mass causes a curvature of space-time. This space-time is a 4-dimensional geometrical construct. An object moving through a gravitational field would deviate from its straight space-like path in order to achieve the closest thing to a straight path in a curved space, which would be the equivalent of a straight line through space-time. Another way to think of it would be that if the object were to follow a straight space-like path, this would result in the object moving to a position further from the center of gravitation. This would require work being done on the object, so the law of conservation of energy would forbid this path, and the path of the object would become curved in order for it to not violate the conservation of energy. I understand that this would apply to an object MOVING through a gravitational field, but I see no reason why this would cause an object initially "at rest" in the gravitational field (such as a cup sitting on a table) to begin falling, unless there were some sort of pressure of space pushing the object down.