We call this SSB for short, Single Sideband Modulation. Before SSB we used straight Amplitude modulation. It was noisy and it used a lot of bandwidth. More specifically Amplitude modulation produced an output signal that used twice the bandwidth of the original baseband signal. This is where I should start defining my terms I expect. More here.
What's a sideband?
Every kind of modulation produces sidebands. A sideband is just the frequencies adjacent to the carrier wave that contain power as a result of signal modulation. Every transmission signal contains more than a single frequency, these are linked together or superimposed upon each other. Everything that isn't the carrier wave is in the side bands.
What's a baseband?
A baseband is a band of frequencies starting at zero reaching up to the to the highest frequency component of the transmission. RF Modulation results in shifting the signal up to a much higher frequency than it originally spanned. In a nutshell, this everything you had before you modulated the signal, or everything you have after demodulating a modulated signal. The reason we shift all these signals away from zero is that lower frequency signals tend to distort. More here.
How's that different from Bandwidth?
Easy. Bandwidth is the same thing but measured from the lowest frequency, if that's zero, higher than zero or even below zero. The RF bandwidth of a signal is usually about twice its baseband bandwidth.
Almost by default Amplitude modulation of a carrier wave results in two mirror-image sidebands, one on each side of the carrier wave. This is called double sideband modulation. The one below the carrier is the lower sideband, the one above it is called the upper sideband. It all seems intuitive now, but 5 minutes ago you had no idea what any of this was. More here.
In 1914 John R. Carson of AT&T invented single sideband transmission. Single Sideband could be either the upper or lower sideband. Before the FRC ever licensed a single AM radio station, John proved that either sideband could carry as much information as the two sides together. this was a revelation.
In 1915 he filed for the patent "Method and Means for Signaling with High Frequency Waves." After much litigation, Patent number 1449382 was granted in 1923 to Mr. Carson. Wait litigation? Yes, at the same time experiments were conducted at the US Naval Radio Station in Arlington an antenna was tuned to pass one sideband and attenuate the other. regardless.. Carson got the patent for AT&T. More here.
What makes this so interesting is that even though it produced a bandwidth savings of 50% it wasn't embraced. This was largely before broadcast applications, so it was used in telegraphy. But at that time message traffic didn't yet require spectrum-conservation. It had to wait until WWII and government intervention to standardize the power and bandwidth saving innovation.