So I created a Cube in Blender and then I created an Empty beside the Cube (in object mode). Now, when I move the Empty around, the Cube follows... Why?
Sounds like the cube is parented to the empty, making it follow it's transformations. You can remove the parenting by selecting the cube and pressing AltP.
Parenting relations can be set up by first selecting the child object(s), and then adding the parent object to selection making it the active object, and hitting CtrlP