The fediverse is a diverse social network that is distributed across multiple platforms.

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Going from the basis to the specific services:

• The ActivityPub protocol defines a protocol - data structures and forms of data transfers
• The Fediverse is a collection of different social networks and services hosting these social networks that can and do connect and communicate with each other
• Various social platform software like Lemmy, Pixelfed, Mastodon implement (“speak”) ActivityPub and are part of the Fediverse
• Anyone willing can run (host) their own instance of these, by downloading and running them
• The platforms have difference interfaces and capabilities, but in one form or another, users can connect and use other platforms despite them being “different”

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For example:

Lemmy is a social platform like Reddit, but anyone can host their own instance. Users can make accounts and create communities on different instances. Users can then follow and interact with communities from other instances.

For example, my account is on feddit.org, but I am posting this comment to !asklemmy@lemmy.world. Because I follow the community, feddit.org fetches and copies the data from that community, and any activity from either side gets communicated to the other. As a result, you on lemmy.world and me on feddit.org can both see and interact with the same community.

Mastodon is a social platform like Twitter. Someone may have their account on mastodon.social, which is one such instance running Mastodon. Despite being a different use-case and interface, they can follow, read, and post to Lemmy communities.

I tried replying to this comment from mastodon.social. I was able to view this post and this comment. I don’t know if the comment will show up or not; maybe lemmy.world blocks mastodon.social comments.

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The Fediverse is the collection of compatible services and networks that can speak and connect to each other.