Federation is when instances exchange information. For example, you posted to lemmy.ml, while using lemmy.world, and I’m seeing this post and replying to you from lemmy.max-p.me. That’s federation in action, in this case with 3 instances involved. It runs on my server entirely in my control, I’m the admin of it. It’s completely independent from lemmy.ml and lemmy.world but they all talk to eachother.
An instance is one website running lemmy. Lemmy.ml and lemmy.world are two examples. There’s hundreds of them, all operating independently and sharing information.
Defederation is essentially when federation is cut off from a given server, think banning an entire instance essentially.
The fediverse is the name of this whole system: it’s federation and universe smushed together, fediverse.
Cross-platform instances would be instances that can talk to multiple platforms. For example, Kbin lets you browse Lemmy threads and Mastodon microblogs from the same place. Mastodon users can somewhat see Lemmy posts. I’ve never seen it referred to as cross-platform though.