A simple jet engine does four things- suck, squeeze, spin and blow. The compressor sucks in the air, the combustion chambers add the squeeze, the turbine is spun (to power the compressor) and the exhaust is blown out the back to provide thrust.
We all know the 707 was the first truly successful jet airliner. And early 707s were powered by the Pratt and Whitney JT3C, the civilian variant of the J57 turbojet. While an excellent engine for its day, it had a couple of disadvantages. First, they had a fairly high specific fuel consumption. While the cost of jet fuel in those days wasn’t a terrific concern, higher fuel consumption meant less range for a given flight. Second, they were tooth-jarringly loud. Like, really, really loud. The Jet Age of commercial air travel wasn’t universally popular, as neighborhoods around airports that previously only had to tolerate the occasional piston powered aircraft overhead now found houses shaking to their very foundations from the stupendous noise of the 707s blasting overhead.
The noise of a jet engine is primarily a function of the average velocity of its exhaust gases. Turbojets take a relatively small volume of air, and accelerate it to very high speed.
Pratt and Whitney, knowing Rolls Royce was working on a turbofan (an idea invented in the Soviet Union just before World War II) decided to modify the JT3C to a turbofan design. A new stage was added before the compressor. This fan would indeed compress air, but critically, this air would bypass the combustion chambers. The effect was a jet that moved about three times as much air, but the average velocity of the air was much lower, meaning the noise levels were much lower as well. As an added bonus, that bypass air tended to form a shroud around the high velocity exhaust that did pass through the combustion chambers, helping to dampen that noise.
As noted, the engine moved about three times the mass of air, though at a substantially lower average velocity. But mass and velocity also determine the thrust of an engine, and that larger mass meant the new engine, the JT3D, had about 25% more thrust overall. And the new JT3D also had greatly improved fuel consumption.
Entering service in 1961, the JT3D was an enormously successful design. In addition to powering hundreds of airliners, it also had a military variant, the TF33, which powered the C-141 Starlifter, and even today flies on the B-52H Stratofortress.