Decompression diving means that the divers absorb so much nitrogen (or other gas) during a dive that it's not possible to ascend directly surface without a substantial risk of DCS. Instead, diver makes a series of stops, each progressively longer, to allow sufficient time for the body to release dissolved nitrogen. 

Decompression. diving usually calls for using special synthetic breathing gases, requires a good deal of surface support. and even when done proper. compared to recreational diving the diver has more risk from DCS and other hazards. Obviously, this type of during is beyond the scope of the course an : recreational diving, though you'll learn - procedures for making emergency decompression stops in the unlikely event you accidentally exceed a no decompression limit.

Dive tables have been around since 1907, and until the late 1980 where primary method for planning dive. Although you'll probably end up using a dive computer for most of 'your diving tables still have their place for two primary reasons. For one, understanding how to plan dives with table gives a "feel" for what your computer does - it gives you a sense (a precise time) of how long a computer will let you stay at a given depth. 

Second, being electronic, dive computers can malfunction on you due to battery failure, impact. baking in sunlight, you name it Dive tables, being primarily printed plastic, are much less likely to file unless your dog chews them up or something. So you'll want to have them along as back up - if your computer crashes on a dive trip. (I tables may mean the difference between being in the water, or sitting at the dock in a very foul mood.

Until 1988, the dive tables recreational divers used were really hand-me-downs from commercial and military diving. Although they adequate for planning recreational dives, they were tables for decompression diving and had to accommodate large amounts of theoretical nitrogen, and consequently "penalized" recreational divers, who by making no decompression dives, had far less theoretical nitrogen. Further more, these tables were tested on predominantly young, male military divers, which didn't fully represent the population spectrum you find in recreational diving.