Tech dive...
Under the covers, DSP converts the digital music signal from time to frequency domain. Now in frequency domain there is a data point for as many frequencies as needed (more needed the higher the resolution) and the signal processing algorithms can now manipulate or transform each frequency as needed.
A simple case would be a volume control. The amplitude of the signal at all frequencies is either increased or decreased by the same amount at all frequencies. Simple addition and subtraction.
Then it gets more complicated from there. A digital equalization operation might focus a boost of a certain magnitude at a certain frequency and control the range of frequencies around that impacted (Q).
Towards the more complex end, you have a room correction algorithm that automatically determines what to adjust at each frequency based on measurements of the room acoustics taken by a microphone.
So you can see how powerful DSP is. Vendors might apply it under the covers in their gear to help better achieve a desired reference sound or perhaps more unique "house" sound or users can optionally do their own tweaking as needed. Dynamite stuff!
Another cool application I can cite is DSP built into active monitors. I have a pair of tiny Vanatoo active speakers that has DSP built in. Why? it allows the sound of the tiny speakers to be tweaked right out of the box to provide results that are beyond what would otherwise be possible with such tiny speakers. I came across Vanatoo at a high end show a few years back where the audiophiles were huddled in mass and aghast at the sound coming out of a pair of tiny $600 speakers. Obviously, I was also quite impressed and bought a pair. One of the best sounds possible these days for a mere $600, and it will probably only get even better over time as the application of DSP technology continues to evolve!