The tables are based on an algorythm that predicts the absorbtion of nitrogen into various tissues of the body. Different tissues absorb and release nitrogen at different rates.
the depth you reach on a dive, coupled with the time you spend there, will determine how much nitrogen is absorbed into the various tissues. After a certain time (dictated by the tissue absorbtion speed), the tissue will become full of nitrogen at that pressure (depth). This is called Saturation.
When you begin to ascend from the dive, your tissues become 'super-saturated'. This means they contain more nitrogen than the external pressure. Our bodies can tolerate a small level of super-saturation...and this allows the nitrogen to slowly leave our bodies (again, this is determined by the tissue speeds). However, if we ascend too quickly, then the super-saturation becomes to great and the nitrogen in our tissues will expand and form bubbles. This is known as Decompression Illness...and can be very damaging or fatal.
The tables used for recreational diving keep the level of nitrogen saturation within our tissues to a minimal level...meaning that a slow ascent to the surface is enough to off-gas the excess nitrogen.
However, if you stay at depth beyond the limits of the tables, then your body will contain more saturated nitrogen than can be safely released on a slow, direct ascent to the surface. In order to allow the release of this nitrogen, the decompression diver must make numerous 'stops' or pauses on his way to the surface.
The deeper that you go and the longer you stay, the more nitrogen will be absorbed into your very slow tissues. This means that the process of letting the nitrogen out will also be very slow. This, in turn, means very long stops on your ascent.
The algorythms used to predict the behaviour of nitrogen absorbtion and release on your body will provide the times and depths for the stops that you require.
decompression diving requires considerable extra equipment, skill and training. This is for 2 main reasons.
1. The dive profile must be planned and run precisely.
2. It is very dangerous to ignore/miss the required stops on your ascent...so if you have a problem on the dive, you must resolve it there...as ascent to the surface is not an option.