Well basically when you modulate a carrier (AM is modulating the amplitude of the carrier with the data signal) half the energy ends up in the carrier signal, and the other half gets split up between to sidebands that sit to either side of the carrier on the spectrum. The sidebands are mirror-images of each other.
There's techniques to suppress them (meaning you don't waste half your transmission energy on redundant signal) but broadcast AM/FM radio doesn't utilize it. Other advantages mean a more efficient use of the spectrum (ie, a whole other signal can sit where the other sideband used to be).
This article should lead you down the rabbit hole
Interestingly, if you use that modulation mode specifically (AM, single sideband suppressed carrier) and tune the oscillator a hair off the mark, you sound just like the X-Wing pilots in the original Star Wars movie...