Arm-wrestling is a contest. Two people sit facing each other, put one elbow on a table, lock hands, and each tries to force the other person's hand down onto the table. The winner is the one who pins the other hand down. It is a show of arm and upper-body strength, often done for fun after a meal, not only as a formal sport. You can also use arm-wrestle as the verb: they arm-wrestled for the last piece of cake. Though actually, good arm-wrestlers win with stance and the shoulder, not only with a big arm — but in everyday talk people still treat it as “who is stronger.”