Well, classically the fourth dimension is time (height, depth, width, and time would be how you plot where something is in space and time). Which you can't see time, so there's that.

But on the general nature of perception, you can only see within a narrow bandwidth of light, and there are colors outside your perception (like ultraviolet and infrared as a very immediately outside the band examples). You can't see radio waves, radiation, etc. The same is true for each other sense you have. Thus, it's "possible" an entire world that we can't perceive exists.