>>11059461A fourth spacial dimension would allow you to "see" the entirety of a volume when stepped "out" perpendicular to the XYZ axis in the same way a third spacial dimension would would allow you to "see" an entire surface when stepping "out" perpendicular to the XY plane.
You also get a degree of freedom in rotations that would otherwise not be possible. For instance, just as you can "flip" an image with the help of a third dimension to invert it, so too can you "flip" a volume in with the help of a fourth dimension to invert a volume. If we put you in a hypothetical 4-dimensional space to "flip" you, you'd come out with your with your heart on the left side of your body, and everything you'd read would seem backwards, and your image through a mirror would look like the "normal" you.
There are other neat things you can do in the 4th dimension. Among them is the freedom to move through 3-dimensional "slices" in space. If we had such a technology, we'd be able to, say, perform non-invasive surgeries by targeting cancer directly without any incisions in the body from the outside... essentially "cutting" out tumors etc and sucking it out through 4th dimensional space. In a similar way you could poke a hole through a center of a circle drawn on a piece of paper without piercing the edges of the circle.
I have no reason to disbelieve 4-dimensional space doesn't exist. In fact, I believe much of the dark matter/dark energy resides in it. I believe gravity transcends these dimensions and it's a fundamental key in unlocking ways to traverse through it.