Mezzo forte is a musical direction to play a section of music at a pretty high volume. If you're playing your flute mezzo forte, you're playing it moderately loudly.
While mezzo forte, abbreviated as mf in sheet music, is on the loud side, it's not as loud as forte and definitely not as loud as fortissimo. Like many musical terms, mezzo forte is Italian. It literally means "moderately loud" or "half loud." It's an intermediate dynamic level that creates a subtle shift in volume to contrast with softer and louder sections of a piece of music.