I would first say it is not correct to say that the table or the computer are accurate (not correct because it might create a fake expectation from users). Accurate (or not accurate) could be an instrument that measures something and gives a measurement, which is not the case here. Both are based on the same concept: combine a theoretical mathematical model of bubble formation with statistics based on how divers reacted to a decompression based on that theory, and adjust the results until you generate a decompression plan that would keep most (as in 99.999...%) of the divers healthy (with no DCS issues). With the current technology, nothing tracks (as in measuring) your real tissue nitrogen loading, or - even harder - if there are any bubbles in your body. Everything is based on the assumption that if so many divers reacted fine to that decompression schedule, you should be fine too. There's a very very small chance that you might react differently for some reason and get bent even you decompressed by that schedule. Of course, the science behind is based on physics laws, so the predictions are very close to the real thing, but still it is not based on real data taken from your body.
The table was the first implementation of this concept. In order to keep it simple, they created a very simple decision process, based on 2 input variables (maximum depth and time). This also had a hidden advantage - it "rounds" the schedule a lot in the direction of added safety - because it provides the same result if you stay 1 minute at a depth of 30 meters and 19 minutes at 5 meters, or if you stay 20 minutes at 30 meters, even though it is obvious your nitrogen loading is way different.
The computer is able to process many more variables in order to get the result. Instead of just outputing a value based on the maximum depth and total time (although I'm sure some of the early computers really did only this), a software inside it simulates the nitrogen loading and off-gasing of a number of "virtual" body tissues, that should theoretically match all kinds of tissues in your body. Because it continuously tracks the behaviour of that virtual (mathematical model of a) human body at the real depth you are, its result is closer to reality. Some advanced computers might take into account things like mistakes in your diving (fast ascents for example) and pad the results with safety margins. I think the only "real" parameter of your body that some advanced computers are measuring is the heart rate (like in the Galileo) - this allows the computer to guess if you are making more effort and then reduce the NDL and extend the stops accordingly.
So, the answer is that the computer tries to provide a result as closed to reality as possible, which extends your allowed bottom time. But keep in mind, it is not 'accurate'. It just predicts closer to edge - and because we are talking about statistics here, it may also mean that the computer might predict a deco profile which may be less than needed for very rare and very specific conditions of your body, in which case you could get bent. Of course, all the studies involved are making this occurence very improbable.
My advice is don't push the limits. If the computer gives you an NDL, try to exit before it. If you go into deco, plan your dives with tables, or use a more conservative computer setting - specially at the begining, when you don't know your body enough to know how it would react. Try to be familiar with table values for the depth of your dive, so you can know if the results given by your computer are reasonable or there's any bug or problem with them. Still, when diving within sound limits, the computer is a very valuable tool to extend the bottom time of repetitive dives, easier than with tables.
hope that helps!
