We find it very hard to conceptualize past the first 3 dimensions of nature, i.e. length, width and depth. Well not really; we are also well aware of the 4th dimension which is none other than time itself. We don't necessarily think of time as a dimension for, we cannot influence time as directly as for example squeezing a ball. The 4th dimension is as much as what the human brain can comprehend for we live in a 4 dimensional world. However there exists a 5th dimension which forms the entire basis of what a select few scientists in the world work on every day - the field of Quantum Mechanics (which Albert Einstein himself refuted as being "unrealistic" given its complex nature). The presence of a 5th dimension would basically mean that for every action that we perform we follow an independent path in the 5th dimension, i.e. every time each one of us make a choice be it our own or influenced by chance or by others, we forge a different path in the 5th dimension. The 6th dimension extends this idea to refer to the possibility of moving between states, i.e. moving from one point in the 5th dimension to another immediately. What this effectively means is that at any given instant in time (i.e. the 4th dimension), there exists an infinite number of parallel worlds representing each possible action in the real world. This assumption is also the basic concept behind the Schrodinger's Cat experiment. As described in Wikipedia:
Schrödinger's Cat: A cat, along with a flask containing a poison, is placed in a sealed box shielded against environmentally induced quantum decoherence. If a Geiger counter detects radiation then the flask is shattered, releasing the poison which kills the cat. Quantum mechanics suggests that after a while the cat is simultaneously alive and dead. Yet, when we look in the box, we see the cat either alive or dead, not a mixture of alive and dead.
An excellent presentation on how to conceptualize the 10 dimensions of nature is available at http://www.youtube.com/watch?v=XjsgoXvnStY and I would highly recommend that you go through this extremely well presented narration. There is also a book by the same folks on the Tenth Dimension whose website is http://www.tenthdimension.com



