The best way I can really explain this is, in a 2D space, two lines are parallel when you can draw a perpendicular line between both of them. In a 3D space, if you have two surfaces that are facing each other exactly, you could draw a normal between them (except when put into function, since both objects have normals, one of them would have to be the opposite of the other, so they could face each other).
It's easy enough to do in rotations like that, but with rotations like this, it's not as easy:
I want to rotate the cone so its base is 'parallel in 3D' and facing the side of the cube. The thing is though, I need a fairly quick method of doing this because I need to do this many, many times.