Music Player Command
Music Player Command (MPC) is a simple command-line program for controlling the Music Player Daemon audio player. It is a command-line utility, not an application. It's used to send MPD simple commands like add that file, play, stop playing and similar commands.
MPC allows you to do a lot of the GUI front-ends can do: Add files to the playlist, play, pause, switch song, etc.
Features and usability
If you are not familiar with the Music Player Daemon: It is a system service which manages and plays music. It is typically managed with a graphical program like Cantata but it can be fully controlled with the command-line utility mpc too. However, doing so is not very practical. At all.
MPC may also be a preferred choice for controlling MPD if you think X11 and this whole GUI trend to be a over-rated momentarily passing fad which is bound to go away eventually. For everyone else it's just simpler to use a graphical program for day-to-day playlist management.
The use-case for MPC
MPC can be used in scripts and things like that. You can assign keyboard shorts to run MPC commands using your favorite desktop environments standard way of assigning keyboard shortcuts. It can also be used to start and stop music playback using systemd timers or cron jobs - which would enable you to use MPD as an alarm-clock.
You can read the manual mpc page here.