This is how a typical AM system transmitter works:
The information signal is mixed with the carrier signal and produces the full AM signal to be transmitted.
Then must process out the carrier by demodulation to reproduce the information signal.
Conventional AM transmission has several problems:
The concept of single side-band (SSB) is very simple: if you don't need two side-bands, get rid of one! To make that happen, you merely add a component to your system that removes the extra side-band. That component is called a band pass filter.
Here's what the SSB transmitter looks like:
Note that the band pass filter has removed the lower side-band (LSB) and the carrier from the spectrum. The remainder is transmitted.
The receiver cannot output the signal as is, it must first restore the signal to what is should be before demodulation. The receiver in a SSB system has its own carrier signal (from a local oscillator) that is puts back in. The receiver looks like:
By having its own carrier signal, the receiver makes the signal back into what would be sent by a conventional AM system. The remaining signal is processed normally.
So, there are two modifications to make it work
By eliminating the duplicated side-band and carrier from transmission, the bandwidth has been reduced by half. The formula for predicting bandwidth in a SSB system is BW = fm, where fm is the maximum modulating frequency used. By reducing the bandwidth transmitted, you may put double the number of channels (or stations) in the same frequency band.
Because the carrier if also filtered out, there is no transmission unless information is being sent. This is useful if you are trying to be covert. The efficiency is also improved considerably. Recall that efficiency was the power in the side-bands divided by the total power. One can argue that since you are only transmitting side-band information then the efficiency is 100 %. While this is true in our definition, it would be inaccurate to say in general, because the usually definition of efficiency measures what is put out compared to what is put in, and therefore includes losses in the circuitry and antenna. A more typical efficiency would be 80 -95 %.
You improve performance but you add complexity and therefore cost. To make the SSB system work, every receiver must now contain its own carrier oscillator. While an oscillator can made cheaply, providing an oscillator that can cover the range of all possible frequencies in your band and be stable does not come cheaply. Therefore, SSB systems are usually limited to things that already are expensive and/or costly or situations where the improved performance is essential (like the military). Perhaps the most common example is television signals. Although the are frequency-modulation (FM) they are also SSB for the same reasons. The added cost is nil because a local oscillator already exists for superheterodyning (reducing the frequency to an intermediate value before processing) for example.