Can someone explain 4th dimensional objects? I'm not sure if I should ask this in mathematics or in physics.
From what I can tell, there are only 3 dimensions: X, Y, and Z. However, I have seen a lot of things about fourth and even fifth dimensional objects. I have tried for a year or two now to wrap my mind around the concept but I never have been able to do so. Can someone please enlighten me?
The thing is you're not supposed to "wrap your mind around" higher-dimensional shapes.

Instead, what happens is that we take a formalism that is made to describe 3-dimensional shapes (which we can understand more or less intuitively), and then we just see what happens when we replace all of the "$3$"s in that theory with "$4$" or "$5$" or more. The outcome of this is occasionally useful, but it's not supposed to be about things that can exist in the world -- the utility comes because the theory can be used to reason about certain problems that are not in themselves about shapes.

With a bit of experience one can gain a more or less reliable sense of when one's intuition about 3-dimensional situations gives valid results about higher dimensions, but the touchstone of that is always what one can prove in the formal model we're really speaking of.
This man can ! https://www.youtube.com/watch?v=M9sbdrPVfOQ :) 

But I never understand I think we have to have a brain in 4D to understand. 

You can also see that :

A conference really interesting Here

And a short video Here