We don't have to think that the world is literaly more than 3 dimensional to understand spiritual planes of reality and physics. A '2D' hologram has information about a '3D' world. I say the 3 dimensions exists inside the 2 dimensions! Same apply to 'Multidimensional Reality' in our 3D 'space'.
But we still can understand this more than mere analogicaly! Every atom forming the objects of our world can revolve around a tiny, microscopic circle as it moves. Points along the circumverence of this circle is de-facto, 'points along another dimensions'. So planes of reality are interlaced together in the same 3D world much like several pictures are interlaced in the same paper in the technique termed 'lenticular printing'.
In lenticularly printed photograph, you may see a girrafe when you view it at one angle. When you change the angle of view, the girrafe disapears and a lion emerges. Same applies to Multidimensional Reality.