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.