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from Millennium Falcon Haynes Manual which refers to the two projections on the bows of all YT-1300 Correlian Freighters as mandibles.
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According to the book "Incredible Cross-Sections of Star Wars: The Ultimate Guide to Star Wars Vehicles and Spacecraft", the mandibles hold various sensors and an anti-concussion field generator. Three is also the freight barge clamp so the YT-1300 can act like a barge or tugboat and push around large cargo. Also on the port mandible there is the shield generator and projector. On the inner side of the mandibles there is a freight loading arm. Click on the image to see a larger version.
Another purpose is for moving freight around, where the mandibles attach to cargo and push them around, as shown here:
The Falcon, like other ships in its class can be used as a cargo pusher. The (canon) Star Wars: Rebel Files has an image of a newer YT-model freighter moving what appears to be a smaller ship.