Your apps stay live. Cancelling doesn't take anything offline, and anything you've published keeps working at the same address.
Nothing changes straight away either. Cancelling takes effect at the end of the period you've already paid for, so you keep your plan until the date shown in Account → Billing → Manage billing. After that you're on the free plan.
Your daily token allowance drops to the free amount. Token packs you bought and referral tokens you earned stay on your account and don't expire, so anything you've already paid for is still there to spend.
The Build Anything badge comes back on your published apps. Your setting is remembered, so if you subscribe again the badge hides again without you doing anything. The install banner is unaffected, since hiding it never needed a plan.
You may need to pick a different model if the one you were using isn't included on the free plan, and the detailed analytics breakdowns stop being available. Connecting a new domain you own also needs a plan.