This summary is not the rule. The rule text controls.
If everyone involved in a case agrees to end it while it's still waiting for a decision, they can file a joint request asking the court to dismiss it. This applies whether the case is on appeal or in some other stage of review. All the parties or their lawyers need to sign onto this request together.
The request has to explain why the case should be dismissed. If needed, people may also have to include sworn statements (affidavits) backing up the facts in the request. Once the court gets this joint motion, it can simply issue an order ending the case, without going through a full review or hearing.
This rule basically gives people a fast, simple way to close out a case when both sides agree they no longer want the court to decide it. Instead of waiting for a full ruling, everyone can settle things on their own and ask the court to formally end the matter.