Same here. I understand perfectly everything that was said in the video but I still don't understand how the fourth dimension quite works.
However, having only heard of hypercubes and not hyperspheres before I decided to see if there was anything useful about them online and I found this video that I just started watching and already 1 min 50 sec into the video something very interesting was said;
> Everybody knows what the sphere is. I'm thinking of a hollow sphere so like a basketball right. That's a two-dimensional surface living in a three-dimensional space. The hypersphere is generalized one dimension up, so in four dimensions you have this three-dimensional space called the 3-sphere or the hypersphere.
https://www.youtube.com/watch?v=krmV1hDybuU
Already this is telling me something that I have not heard before, and which I find much more helpful than talking about what a shape looks like from the perspective of someone living one dimension further down. That being said it was still useful having that explained as well, which is what Flatland: The Movie (2007) was about as well. Just this fact I quoted above was even more useful IMO.