This is a mug shaped like Wilson the Volleyball, a prominent set piece in the film Castaway (2000), starring Tom Hanks.
In the film, Chuck, a FedEx worker, is stranded on a desert island after a plane crash. While attempting to start a fire, Chuck cuts his hand. He furiously throws several objects from the salvaged FedEx packages washed ashore after the crash, including a Wilson Sporting Goods volleyball, and leaves a blood-stained handprint on the ball. After calming down, Chuck draws a face into the smeared blood, names the ball Wilson, and begins talking to it. He continues to talk to it regularly during the rest of his time on the island.