An instance is a server running the Lemmy software (or some other federation software such as Mastodon, Kbin, Pixelfed, and others). Instances can talk together (similarly to how you can send email from gmail.com to outlook.com), so you can sign up on one instance and subscribe and comment to communities on other instances
What’s a community?
A community is to Lemmy what a subreddit is to Reddit. on
What are federations?
Federation is the machanism allowing different instances (servers) to talk together. Federation is automatic, so two instances becomes federated, when you as a user on one instance subscribe to a community on a different instance
Whats the difference between all these?
Many instances are general but have somewhat different values and rules for what you can post or not. "lemmy.world" is a good choice for a general instance. There are also topic specific instances, such as "mander.xyz" that is science focused.
What’s mastodon?
Mastodon is like twitter but is part of the federated universe (the "fediverse").
What’s Kbin?
Kbin - like Lemmy - is like Reddit. The impelemntation is different and focuses on different fetures. Some (myself included) like Kbin more than Lemmy - others the other way around.
What’s ActivityPub?
ActivityPub is the common technical protocol that allows all of the software in the Fediverse to talk together. Both Mastodon, Kbin and Lemmy (and others) are build "on top" of the ActivityPub protocol.