This summary is not the rule. The rule text controls.
If you and the other side in a case work out an agreement about how to handle part of the proceedings, that agreement needs to be in writing and signed by the person who is agreeing to be bound by it. This protects everyone involved. Without a signed written agreement, one side cannot later claim there was a deal if the other side denies it or the court has no way to check.
There is one exception to this rule. If you make an agreement out loud in open court, or during a pretrial conference with the judge, that agreement counts even if it is never written down. The court record of what was said serves the same purpose as a signed document.
The point of this rule is to avoid arguments later about what was actually agreed to. Verbal promises made outside of court, or informal understandings between attorneys, will not hold up unless they meet these requirements. If you want to make sure an agreement with the other side is enforceable, get it in writing and signed, or make it part of the official record in court.