Your Avenue is private until you publish it, and the switch sits at the top of the card, with the word beside it saying where you stand: Live or Private.
You need an Avenue Name first, because the name is the address. Until you claim one the switch stays disabled.
Two controls sit next to the switch. One copies your Avenue link, ready to paste. The other opens the page: before you publish it opens a preview, so you can read the real page exactly as a visitor would while it is still unreachable by anyone else. The preview works before you have claimed a name, which is when it is most useful.
Turning the switch back off takes the page down. Someone who already has the link then sees the same not-available page as someone who guessed at a name, and so does a visitor to an account that has been suspended. The three are deliberately identical, so the page never confirms whether a name exists.
Changes save as you make them rather than behind a Save button, so the page a visitor loads is always the one you last edited.
Your Avenue follows the account. A cancelled or suspended account takes its Avenue offline along with every share link, and both come back when a plan is active again.