Fediverse is an interconnected network of different services like Social Networking, Microblogging, Blogging, Video Hosting, File Hosting, and other services which can be independently hosted on different servers but can still communicate with each other. A service client can have multiple (hundreds and thousands) servers across the globe (called Instances) where each Instance (Server) has their own rules and regulations. And since all the servers are running on a same base communication protocol they can communicate outside the boundaries of the servers and instances too. These services are connected in such a manner that a video hosting platform can communicate with a photo sharing platform or with a microblogging platform or any other platform. Every platform on fediverse can communicate with any other platform on the fediverse if they use the same communication protocol.
One of the most famous communication protocol of fediverse is Activity Pub. It is implemented on different softwares like Mastodon, Pleroma, Nextcloud, Peertube etc. There also are different communication protocols like Disapora Network, Zot and OStatus implemented on softwares like Friendica and Disapora*.
These softwares are open source and anyone can create their own server if they have sufficient will and resources.
You can find me on a microblogging platform inside the fediverse called Mastodon : @email@example.com