To speak in a convincing and persuading manner, usually to make a person do something they wouldn't normally do. A person who is or has a mouthpiece is usually attributed to as a playa
or a lawyer.
-Man that guy sure has a mouthpiece on him. I tried picking up those two girls and he's walking away with both of them.
-Hey, i just convinced my girl to do anal.
-What? Isn't she like really religious? Man that's some mouthpiece on ya.
-You know that lawyer who got O.J. off the hook? That guy's a hellava mouthpiece.