One example that gives you an idea about four dimensional space is plugging in a USB. Sometimes you try plugging in a USB and it doesn't fit. You then twist it 180 degrees and it still doesn't fit. You then turn it another 180 degrees (which makes a full 360 degree turn) and it works. Now obviously you didn't push hard enough or something the first time but this scenario gives a concept of four dimensional space. At every point in space there are actually two points. We are surrounded by more than 3 dimensions but as far as I am aware we cannot access the fourth of fifth dimension. If we could, we might actually have to turn the USB cable 360 degrees to make it work even though it looks like it fits the first time. This would be an example of rotational 4D forces. The fourth dimension can actually be thought of as time as well as it was in Interstellar.
Movie link: http://movietube.cc/watch.php?v=lq85UpnQMZI
Anything that is fifth dimensional or above is hard to understand. You can read the article below if you wish which briefly explains the basics of the fifth dimension. My understanding is that in the fifth dimension time is tangible and you can see every possibility of the past, present, and future. There are several dimensions after the fifth, each getting more and more complex. To prove the complexity there is an image below which is a visual representation of the fifth dimension. While we cannot see or understand the fourth or fifth dimension, we can transfer it into terms we can understand. There is no way to truly understand the fourth of fifth dimension because we cannot physically imagine it. I believe eventually we will be able to comprehend the fourth dimension and even be able to use it's properties. This may happen through evolution or through scientific/computational breakthroughs. We will have to wait and see what the world has to offer.
http://www.bustle.com/articles/47537-what-is-the-fifth-dimension-in-interstellar-how-to-understand-the-films-complicated-physics
Image credit: Wikipedia, Five-dimensional space