[Paul Maine] was experimenting with GNU Radio and an RTL-SDR dongle. He created an SSB receiver and, lucky for us, he documented it all in a video you can see below. He walks through how to generate SSB, too. If videos aren’t your thing, you can go back to the blog post from [Gary Schafer] that inspired him to make the video, which is also a wealth of information.
There is a little math — you almost can’t avoid it when talking about this topic. But [Paul] does a good job of explaining it all as painlessly as possible. The intuitive part is simple: An AM signal has most of its power in the carrier and half of what’s left in a redundant sideband. So if you can strip all those parts out and amplify just one sideband, you get better performance.