For years, most racing bikes came standard with a 53/39 crankset. This served most racers and enthusiasts well, but made climbing difficult without swapping out the cassette for something like a 12-27 or even a 11-34 (mostly used on mountain bikes). As road racing bikes became more mainstream, it became clear that the 53/39 wasn't serving the vast number of average riders very well. It also wasn't very practical for the rider in hilly or mountainous areas who didn't have a team mechanic to swap out cassettes for them.
To accommodate the non-competitive rider who was beginning to shell out serious cash for the latest in bike and component technology, manufacturers began selling more and more bikes with triple cranksets. The road triple was basically a standard double with a third chainring on the inside for a 53/39/30 set up. This gave riders a much wider gear range than the standard double and thus the ability to tackle a wide range of terrain. The triple gave newbie roadies the freedom to hammer big gears downhill and on the flats, but also the ability to handle steep climbs with ease.
The triple was great, but despite it's versatility, there were several downsides. In order to accommodate the 53/39/30 set up, component makers had to create special derailleurs to handle the wide gear range and sometimes special shifters. As technology got more complicated it also got more difficult to maintain. Even riders who adjusted derailleurs on a weekly basis found it hard to keep a triple in smooth working order. There were also many duplicate gear rations and the extra chainring added more weight to the rotating mass of the crankset.
Around 2003 more and more bike makers started offering bikes with compact double cranksets. The compact double was usually set up in a 50/34 configuration. You lost the huge gears at the top end (which was not a major concern for most non-racers) and came in between the 39/30 rings of the triple with a 34. The 34 small ring, combined with an 11-25 or 12-27 cassette gave riders the climbing ability of a triple with the simplified shifting, lighter rotating mass, and straighter chain line of a double. The compact double was gradually adopted by more and more recreational riders and racers alike. Now major component manufacturers like SRAM don't even offer a triple in their lineup of cranksets.
Most riders who don't compete and who live in moderately hilly areas will see many advantages in the compact double over the triple and won't miss the big gears of the 53. Maintainance will be easier and you get a lighter weight component to boot. The only riders who might benefit significantly from the triple are those embarking on long distance loaded tours. You probably want the widest possible gear range on a tour and the lowest possible gears if you're hauling massive weight up steep mountain passes.
If you're a recreational rider looking for an efficient and versatile crankset, the compact double is a great option.