A .mpc file is a Musepack music file, a popular high quality lossy compression that offers higher audio quality than MP3. Musepack is based on the MPEG-1 Audio Layer 2 standard (MP2), but includes many improvements. It is believed by audiophiles to be one of the highest quality lossy compressions available for music.
Foobar 2000 is an excellent software audio player that supports Musepack. If you wish to burn Musepack audio files as an audio CD, you can download a plugin for MPC files for Nero Burning Rom here.
Related software tools
Foobar 2000 (Freeware)
Foobar is an advanced audio player for audiophiles
Nero Burning ROM (Shareware)
Nero is the best and most complete DVDR / CDR / Blu-ray all-in-one software