In the new lesson experience, publishing is its own step. The version of a lesson that students see isn't whatever's in the editor right now. It's the snapshot you published last.
This matters because it means you can keep editing without disturbing anyone who's mid-lesson.
Publishing for the first time
Click Publish in the top right.
The current state of the editor becomes a published snapshot. Any classroom you assign the lesson to from this point on will see this snapshot. Students start working through it.
Editing after publishing
Open the lesson, make your changes, and your edits save automatically. Students keep seeing the published snapshot, not your work-in-progress.
There's a small "Unpublished changes" indicator next to the title to remind you that your latest edits aren't live for students yet.
Publishing a new version
When you're happy with your changes, click Publish again. The editor creates a new version and shows you a confirmation dialog:
Push to existing classrooms updates everyone, including students who are currently mid-lesson. Use this for typo fixes and clarifications.
Only new classrooms keeps existing classrooms on the old version. Use this when the change is significant enough that you don't want to disrupt students who are already most of the way through.
You can change a classroom's version later from the lesson assignment settings if you change your mind.
Why versions matter
Versions give you space to keep improving a lesson without breaking the experience for students working through it. A small typo fix doesn't need a new version pushed to every classroom in your school. A complete rewrite of the question bank probably does.
Treat each published version as a stable thing. The editor is your workshop, Publish is when you hand it over.
Preview vs Publish
Preview lets you walk through the lesson exactly as students see it, without affecting anyone. Edits in Preview don't change the published version. See "Previewing a lesson before students see it" for more.
Publish is what students actually receive. The two are separate on purpose.