To muffle is to quiet a sound, usually by wrapping it with something. If you try to speak with a scarf over your mouth, your voice will be muffled.
When a hitman puts a silencer on a gun, he's muffling the sound of gunshots, since muffling makes things quieter. Usually, muffling involves wrapping something around or putting something over a noisy thing. Muffling dampens, tones down, deadens, and dulls. Also, if you hold down your emotions and don't express them, you're muffling them. Muffling keeps things quiet.