"Adaptive sampling" (AS) works like the name implies. After a number of render iterations, AS looks at the image, and measures how much noise is left, and where. It then concentrates the next rendering iterations on the areas that need more work, instead of spreading it across the entire image. So it is a more intelligent approach, targeting ray casting processing to areas that need it more, and hence speeding up the render by periodically inspecting the current image noise to know what to do next.
As a result, you will notice rendering progress works differently when AS is enabled. No matter how high the pixel samplers you enter, AS will stop the render when the noise is below your desired threshold. You determine that by the only parameter AS requires, where the default is zero. The higher the value, the more tolerant AS becomes to noise in the final render, and also the shorter the render times.
There is a limit to how much noise the human eye can perceive in renders. I can't recall the average number, but I think it was something around 11% (from the back of my head). The bottom line is that we cannot see noise below that threshold, so the AS parameter should be set according to that. But mind you, noise in your render comes from many different factors, like for example, how well lit the scene is, or how many materials have things that need raytracing, like SSS, transparency, shadows over transparency, caustics, translucency, and refractions.
However, please keep in mind that AS cannot do magic. Each scene will require more or less pixel samples to clear the noise. AS just makes it quicker to do that, assuming we gave it at least enough pixel samples to begin with. The render will stop depending on which condition was reached first - the pixel samples limit was reached, or the AS noise threshold was reached - which ever happens first. The worst that can happen is when the pixel samples limit was reached first, which might leave more noise in the image than we had wished for. So a general recommendation is to aim higher with pixel samples when using AS. It will automatically end the render when the noise threshold is reached, which might skip much of the excessive pixel samples we had requested.
Hope this helps.