Dimension as a word means a measurement of some particular spacial extent. What does it mean in pratice though? Well, two things:
1. It gives as a way to measure objects in nature by using the 3-Dimensional grid (lenght, height and width). An object ideal to be presented on a 3D grid is a cube or a cuboid. If you placed one of it's corners on point 0 of the 3D grid, it's edges would show you the three axes XYZ representing the three dimensions of the cube/cuboid.
2. Thanks to the 3D grid we are also able to better place objects in space, create 3D models and whole virtual worlds using the CGI. It gives a way to create perspective on paper as well.
There's a very interesting thing about dimensions and it's called 'alternative dimensions'. Some scientists and Sci-fi passionates believe that there can be an unlimited number of dimensions which leads to belief that there are also alternative worlds similar to ours but different in details. Also, some believe that Time is the fourth dimension and therefore it might be possible to travel through time.
If you want to find out more about other dimensions I would suggest you look for talks about The String Theory for example. It's extremely interesting.