sudo apt install pavucontrol
It lets you configure some neat tricks. For example, you can setup an audio device that forwards to another computer running PulseAudio, an RTP receiver, and a few other similar protocols then set say, Spotify to output to that device. So if you have some network-enabled audio receiver somewhere in your house/office/whatever you can send audio from your Linux workstation to it.
You can of course also pass that audio through various filters/plugins to mess with the sound before it goes out to the remote receiver. For example, equalize it, noise removal, etc. PulseAudio supports LADSPA plugins so if you wanted to you could setup a little Raspberry Pi audio receiver at your front door and yell at solicitors in a robotic voice from your desktop. All with a bit of PulseAudio configuration fiddling =)
I remember trying it on whatever Windows computers were in the lab just to make sure I wasn't crazy and that this wasn't there all along, and sure enough, they kept the same volume no matter whether the headphones were plugged in or not.
One of the first PulseAudio victories I remember, at a time when I vaguely recall that it was a newcomer and people were really pissed at PulseAudio's bugs and recommending just straight ALSA instead.