Audio is transmitted via radio waves, with audio being impressed on a radio signal using a method called modulation. The two types of modulation that most everyone is familiar with is AM (amplitude modulation) and FM (frequency modulation). This is where the name of these broadcast bands are derived from.
An AM-modulated radio signal consists of a continually broadcast base signal (the carrier) and two modulating signals, called sidebands. The audio you hear on an AM broadcast station is from the two sidebands. Even when an AM station isn’t transmitting audio, you can still tell a signal is present, which is the carrier. The two modulating sidebands containing the audio are located on both sides of the carrier. The one just above the carrier frequency is called the upper sideband, while the one just below it is called the lower sideband.
Over time, radiophiles figured out that you could separate and strip out the carrier, and transmit using one of the sidebands, which was called (you guessed it) single-sideband. Single-sideband transmissions can be either the lower sideband (LSB) or the upper sideband (USB).
When broadcasters transmit AM radio signals (music being a prime example), they need the best fidelity possible so that listeners will stay tuned to their station. To achieve this high fidelity, they use the carrier and both sidebands, resulting in roughly half of the transmitter power being wasted on a blank carrier, with the remaining power being divided by the two sidebands. A single-sideband radio removes the carrier and one sideband, concentrating all of the power or energy into the remaining sideband. What this means from a power perspective is that a 150-watt SSB transmitter puts out the same power as a 600-watt AM transmitter (300 watts of carrier + 150 watts on each sideband).