It means someone who talks a lot! The phrase pretends the mouth is a pair of legs, and these legs are moving so fast/frequently that they are running away (from the face), hence 'RUN your mouth off your face'. Hope this helps!

Someone who runs his mouth means that they keep on talking on a subject that is causing distress to others and provoking a fight. You can also say that that person has a big mouth, they are a big gossip or that they insert their feet in their mouths.

In Turkish i know :))