Common knowledge is information that everyone knows and, importantly, that everyone knows that everyone knows, and so on, ad infinitum. If information is common knowledge in a group of people, that information can be relied and acted upon with the trust that everyone else is also coordinating around that information. This stands, in contrast, to merely publicly known information where one person cannot be sure that another person knows the information, or that another person knows that they know the information. Establishing true common knowledge is, in fact, rather hard.
Related Pages: Public discourse, Consensus, Inferential Distance
External posts:
The Kolmogorov option by Scott Aaronson
kolmogorov complicity and-the parable of lightning by Scott Alexander