Why, for example, should we suppose that just because our minds can only apprehend three dimensions (four, if you count time) that that's all there are? Could the world not consist of numerous dimensions that we can not only not perceive, but not even be capable of imagining? Could there not actually be entire worlds integrated with our world but closed off to us because our minds lack the necessary structure to perceive them?
One way to imagine what reality might be like if there actually are more than three dimensions of space is to think of ourselves as living in a two-dimensional world, a flatland, that's visited by a three-dimensional being as illustrated in this short video:
If we actually do consist of more than three dimensions we would look completely different to a being who could perceive those other dimensions than we do to each other. There could quite literally be, in other words, far more to us, and to reality, than what meets the eye.