means To speak so quietly or unclearly that your words blur into an indistinct murmur, hard for anyone to make out.

from From Middle English mumlen, meaning to mutter or eat in a slow, lip-closed way. It's an imitative word — built to sound like the very thing it names, the soft closed-lipped hum of someone talking through 'mum.' It shares a family resemblance with 'mum' (silent, as in 'keep mum') and 'mumble' may be a frequentative of that root, the verbal equivalent of doing it over and over: mum-mum-mumbling.