Here is a classic example of a two-sided market: credit cards. Each transaction is an exchange of value between a consumer and a producer that goes through the platform, enabling it to skim off some of that value. One job of the organization managing the platform is to maintain the conditions that enable the aggregate value seen by both sides to grow sustainably. The book contains an extensive discussion of this job.
An important feature of a two-sided market is that it exhibits network effects. That is, enlarging the population on either side increases the incentive to participate on the other side, adding value to both sides.