PulseAudio is what most modern Linux distributions use as a sound server, the part of the sound subsystem that sits between applications and the sound driver supporting features like allowing multiple applications to output sound simultaneously. PulseAudio adds various features not present in other Linux sound servers like per-application volume controls and easily outputting to different audio devices (for instance, using HDMI audio instead of the normal audio jack).
PulseAudio can be controlled using
which is a GUI audio mixer. It shows a volume meter and control for every
application producing sound as well as an option to choose which audio
device it is outputting to. It additionally lists all of the hardware
input and output devices, as you would expect from an audio mixer.
If PulseAudio is not working properly, you can restart it by running
$ killall -9 pulseaudio
No, really, that's what Debian's PulseAudio page says to do.
When I initially installed PulseAudio, it didn't have my sound cards listed and just had the default null outuput, making it not very useful. Running that command to restart it fixed it.
PulseAudio seems to mute my sound card all by itself. Currently, I just
pavucontrol and unmute it.