Mastodon is an open source federated micro-blogging platform.

The Mastodon documentation site https://docs.joinmastodon.org/ pull covers what a microblog and federation are:

Similar to how blogging is the act of publishing updates to a website, microblogging is the act of publishing small updates to a stream of updates on your profile. You can publish text posts and optionally attach media such as pictures, audio, video, or polls. Mastodon lets you follow friends and discover new ones.

Federation is a form of decentralization. Instead of a single central service that all people use, there are multiple services, that any number of people can use.

• homepage https://joinmastodon.org
• blog https://blog.joinmastodon.org/.
• github https://github.com/tootsuite/mastodon
• patreon https://www.patreon.com/mastodon

The About statement on the Patreon from the main developer Gargron is also a good description:

I'm working on Mastodon, a free, open-source social network server based on open web protocols like ActivityPub and OStatus. The social focus of the project is a viable decentralized alternative to commercial social media silos that returns the control of the content distribution channels to the people. The technical focus of the project is a good user interface, a clean REST API for 3rd party apps and robust anti-abuse tools.

The entire network is like an unlimited number of different Twitter websites, users of which can follow each other and interact regardless of which Twitter website exactly they are on. This has obvious benefits as there is no single company that has a monopoly.