I will try to explain it this after noon after I get home from work.
ok, here we go. When producing a complex mixed signal, such as what you hear on your AM Radio band, the last stages include a mixing stage. this is where two different frequencies are put through a non- linear device such as a transistor or tube, consisting of an audio signal and a radio frequency.
The output will have 4 frequencies: the two original frequencies, one audio, one radio frequency or RF, and two other signals: Rf + Audio and RF - Audio. These are upper sideband and lower sideband respectively. Your AM radio station transmits a signal consisting of the RF [AKA the carrier], and two sidebands and puts energy into all three frequencies to transmit them.
In single sideband, The RF and unused sideband are all filtered out leaving only the sideband signal to have ALL power applied to it and it can travel much, much, much [ad infinitum] further on the same amount of power.
When receiving the signal, the original carrier is added back in and delt with as a regular am radio signal. HOWEVER, and this is important, if your reciever is not equipped to process a single sideband signal it will sound like that signal you heard.
as for being a radio nerd, yes I am. This is what I did in the USAF - I fixed aircraft radios. This is the very basic of explanations, I hope I made it understandable.