In a nutshell, what is single side band?
Without getting to technical, SSB (Single Side Band) is a form of modulation. A source of electromagnetic energy (radio waves) is not the intelligence (sound, data, image, whatever you want to send) itself, it is just a way to carry the intelligence. When radio waves are generated they can be "modulated" with the intelligence that you want to send, you superimpose the intelligence on RF energy so that it rides on the RF. There are many different ways to modulate the RF energy, each has a different name.
You are familiar with the terms "AM" and "FM" when it comes to radio, like an AM or FM radio to listen to music/news/sports? They are two different modes (ways) of modulation. AM means Amplitude Modulation, FM means Frequency Modulation. They are not compatible. To understand what is being sent on an AM transmission you must have an AM capable receiver. To understand what is being sent on an FM transmission you must have an FM capable receiver.
SSB is another mode of transmission. It has greater power density than AM and is much narrower banded. This means it is more efficient than AM, better for long distance communications. There are actually two types of SSB, one is USB (Upper Side Band) and the other is LSB (Lower Side Band), SSB means only one of these is used at a time. DSB (Double Side Band) happens when you transmit both USB and LSB at the same time.
On Short Wave the common modes of modulation are AM, USB, LSB, and CW (CW is Morse Code). Broadcast stations, like Voice of America or Radio Moscow, are typically in AM. Most of the other types of voice transmissions, ham radio operators, aviation, maritime, etc, are in SSB, most commonly USB but LSB is also used. Numbers stations use a mix of AM and SSB, some are one mode, others are another.
Ideally you want a radio with AM, USB, and LSB, possibly CW also, although you can receive CW traffic in USB or LSB. Some radios have only "SSB", while this will work to receive USB, LSB, or CW, it is not as good as a receiver with dedicated modes.
Hopefully that did not just confuse the matter further.
T!