Huh, learn something new every day.A Keynesian beauty contest (originally used to describe stock market behavior iirc) is basically a thought experiment wherein people are shown a hundred photos and asked to pick the ones that they like the most. The catch is that people who pick the most popular photos have the chance to win a prize. The result of this catch is that instead of picking who they think is the most beautiful, they have an incentive to game out who everyone else is going to find the most beautiful so as to try and win a prize.
So in this context, it means that voters (you've probably seen polls indicating that "can beat Trump" is more important to people than "someone I agree with") are picking Biden not necessarily because they like him the most, but because they think other people will vote for him instead of Trump. For example, there are plenty of posters in this thread alone that are closer to Sanders on policy, but either don't like him personally (or 'Bernie Bros') or think he's too risky in an election against Trump.