A murmur is a quiet, blurred sound often heard from a distance. It can be comforting when you're little to fall asleep listening to the murmur of your parents talking downstairs.
Murmur can also be a verb that means the same as mutter: you say something so quietly that your words can't be understood. You might be complaining about something — a murmur is often a sign that someone's not pleased. A heart murmur is an abnormal heart sound that can only be detected by a doctor with a stethoscope, it's so low and soft.