The Fediverse is a collection of services (apps, websites, etc.) that adhere to a collection of open protocols like ActivityPub. By communicating via these protocols, the sites in the fediverse allow users of other platforms to see, interact with, and and share content hosted on other platforms from an account hosted on any other. This openness and interoperability allows users to interact via a service provider with community rules they agree with, without losing access to the greater ecosystem. As I understand it, this leads to more online communities that are more cohesive (because people choose instances that make sense for them), diversified (because anyone can form an instance), and interconnected (because picking an instance doesn’t cut you off from the rest of the fediverse.)

Wikipedia's diagram of the Fediverse