So I've seen a lot of confusion over what exactly that "Hardware Acceleration" button means down in the bottom of the advanced settings of Spotify on PC, with no particularly satisfactory answer ever given that I can find. While it appears that over the past couple years that curiosity had died down, I thought it worthwhile to post a very quick and basic overview of what that switch does.
Inside of your computer (every computer), there is a chip about an inch squared in size called a CPU, which performs the daily tasks of everything that you do on your computer. Along with your CPU (and also having potential roles in audio hardware acceleration) include your motherboard and/or discrete sound card if you have one.
Inside of that CPU, most of it is designed for general purpose computing, a typical sequential set of possible instructions that let you do anything and everything that you need to do, including music decoding and playback. In the case that you are (more or less) using this set of general instructions for such a task, you have what could be called "software" playback, where the software does the majority of the algorithmic work in order to achieve that task.
However, also oftentimes present in your CPU/motherboard/sound card are small sections of hardware *specifically* designed in order to complete a specific task. Oftentimes, this hardware has very little usage outside of extremely specific tasks, but can usually do those tasks much much better than general purpose instructions ever could, due to specific optimizations that can be made, thus the term acceleration. You could have this akin to having a general human or worker who is perfectly capable of digging holes in the ground, but is not nearly as effective as a digger, which is VERY good at digging holes in the ground and not much else.
Some other good examples of hardware acceleration include integrated/discrete GPU's (whose calculations COULD THEORETICALLY be done in general purpose computing, for a massive performance penalty) or video decoding acceleration (as is present on the Broadcom CPU's embedded in Raspberry Pi's, and which allow such a tiny chip to achieve genuinely high-quality video playback).
Enabling hardware acceleration in Spotify will cause Spotify to use those specialized pieces of hardware present in your CPU/motherboard/sound card in order to decode and play back the audio stream. Disabling hardware acceleration will still decode the audio stream using hardware, but it will do so using general purpose computing and software-driven algorithms - a potentially slower approach.
Right so, for what this means for the end-consumer, the answer is, not a heck of a lot. For those with significantly weaker hardware, toggling hardware acceleration can either increase or decrease your listening experience, potentially causing skips and other such issues. It may also lead to a nearly negligible difference in CPU usage as well. Otherwise, for the vast majority, this setting really has little to no impact to the lives of the listeners, which is why it is buried at the bottom of the advanced settings, so that no one would ever have to worry about it, ever.
I hope this sheds some light and relieves some minds out there as to what that mysterious toggle does, and may you all have a wonderful day.