Immediately, you'll be taken through what's basically a hearing test. High- and low-pitched beeps will play, and you'll confirm whether or not you hear them. It's a judgment of your hearing, but also of your headphones. (So, don't get upset if you don't always hear the beep.)
When you're finished, two graphs will appear, one for your left ear, and one for your right. Take a look at them to get a visual sense of what your hearing capabilities are like with and without Adapt Sound. The x-axis shows pitch (frequency), and the y-axis displays hearing ability.
If you're skeptical, you can preview what the sound output is like with and without the Adapt Sound adjustments. Below the graph, hit "Preview Adapt Sound" and toggle between Original and Personalized to hear the difference.
Back in the settings window, you can tell Adapt Sound when to personalize the sound output. Below that, don't forget to indicate your "frequently used side so that it can "adapt" when you've got your phone to your ear.
Revisiting the setup
As Samsung explains, the results produced from setting up Adapt Sound in a very quiet environment should let you get away with never touching the feature again. But if you want to get the most out of the feature, take the short hearing test again when you get new headphones or settle into an entirely new environment.