and I wonder what the advantage is vs. MDP. It was a pretty ok "product" when I ran it 10years ago on an old Pentium III notebook with 256MB of memory. I think it still would work if I booted it now.
The "D" in MPD stands for daemon — so typically it is something where you have a "jukebox"-style computer hooked up to some sound system and multiple (network) clients that can control the playlist etc. MPD is basically a audio player with playlist managment that exposes all controls via network API.
The client could be an app on your phone, or a web-frontend served from that jukebox server etc.
We have a box like that at work, where multiple people are meant to add music, stop and queue it without having to stand up.