Mezzo piano is a musical direction to play a section of music at a moderately low volume, or fairly quietly.
If you're directed to play your violin mezzo piano, you're to play it pretty softly. While mezzo piano, abbreviated as mp in sheet music, is on the soft side, it's not as soft as piano, "soft," or as pianissimo, "very soft." It's an intermediate dynamic range between soft and mezzo forte, "fairly loud." In Italian, mezzo piano means "half soft" or "medium soft."