This summary is not the rule. The rule text controls.
If you want to challenge a jury verdict or ask for a new trial based on certain reasons, like juror misconduct, newly discovered evidence, or errors during the trial, you have to put your request in writing. You can't just make the request verbally in court.
For some specific reasons (like claims about jury misconduct, new evidence, or other similar issues), both sides can use sworn written statements, called affidavits, to support or fight against the motion. These affidavits act as evidence. The court will then handle the hearing following the standard process outlined in rule 1.431(6), which sets the rules for how these types of hearings are run.
In short, this rule tells people that certain trial-related requests must be written down, and gives both sides a way to back up their arguments with sworn statements instead of just verbal claims.