It an apparent attempt to test the authenticity of their prizes.
In their pure forms, gold and silver happen to be very soft metals—soft enough that you should be able to mark them with your teeth. According to the Mohs hardness scale—which relates pairs of materials according to which one will scratch the other first—gold scores a 2.5 and silver, which is harder, a 2.7. Dental enamel rates somewhat higher, which means your teeth will scratch the precious metal and not vice-versa. (Don't try picking at your medal with your fingernails—they have a hardness of only 2.5.)
In principle, you could use the "bite test" to see if a medal were pure, 24-karat gold, as opposed to a less valuable alloy. The less pure the gold, the harder it will be; you certainly wouldn't want to bite down on gold-plated iron. There are some exceptions to this rule: If you bit into your medal and really made a mark, you might be holding a painted hunk of lead. Lead has a Mohs rating of 1.5, which makes it even softer than gold.