I know that when a light ray refracts towards the normal, it means that it's perpendicular. But what is it refracting towards the normal with respect to?

Answer 1

With respect to the direction of the original path in the original medium.

Now clarification: IT does not always bend towards the normal. That is only true if it is going from a medium of lessor index of refraction to a medium of higher index. If the opposite is the case, then it bends away from the normal.