There are (generally speaking) four types of modern bike cranks: single, with one front gear; triple, with three front gears; standard double, with two front gears, and lastly, compact, which is a double with smaller diameter chainrings.
The difference you are describing is between a standard and compact double. A standard was once 52 (or 53) paired with a 42 (these are the count of teeth on the chainrings). In more recent times it became 53/39. Because of the bolt pattern on the crank arms, which back then was often 144 or 130mm, the smallest you could fit was 39.
However, someone revived the 110mm bolt pattern, often used on inexpensive bikes from the 70s and 80s, as well as some oldwer mountain bikes, and some pretty decent cranks as well. This allowed one to use a chainring as small as 34 teeth.
And this allowed one to employ a "compact" front gearing; smaller chainrings; 50 instead of 53; 34 instead of 39. The result? Really no need of that inner granny gear, especially with some minor tweaks to the rear gearing, since the inside gear on most triples was a 32 (I had a mountainbike 28 on mine 'cause i cheat).
The main advantage of compact double over triple was in shifting efficiency. Triples don't shift as well as doubles (which is why you are seeing the growth of compact or even single chainring mountain bike setups too) and also they weigh a little more. For serious riders it's a benefit. I love my new compact, but I don't like the new trend to stack more and more gears on the back. Range rather than number works there. Companies are coming out with 11 speeds now. But 8 was optimal IMHO.
For riders, it allows easier climbing and better shifting. But it's a style thing too for the companies selling it, because except for touring bikes there is a cultural perception that doubles mean "fast". So it plays on customers egos, all those guys that want to look like racers. But at least it's also got a real mechanical advantage for us riders, unlike some things, like bb30 bottom brackets that are nonadjustible and creak, or... remember 20x700 tires?