Take for example a drawing on a piece of paper. That has height and width but does not have any depth. We all know that there is depth in our universe, it's just that a drawing cannot perceive this. Take again that drawing and turn it into a flip book. This drawing now has another dimension, time. The possibility of a high dimensional being, being able to see and travel across multiple dimensions, including our own, is amazing.
Have a look at a simple way of imagining extra dimensions.
Take a point. This is a zero dimensional entity, having no width, no height, no depth, no change over time. Nothing.
Now we have 3 dimensions we can model in real life. Let's have a look at a fourth. Time. Before we can do this we must take everything we have already looked at and correlate it to a single point. This point represents a position in a 3 dimensional universe. A single point in time, the 4th dimension.
So there you have it. An imagination of the 10th dimension.
I hope those of you that got this far did not get lost...
Those that did, I'm sorry.
This guy explains it much better.