What does this motion of dismissal for failure to prosecute under fla.r.civ.p.1.420(e) mean for the petitioner

It means that their case may be dismissed unless action is taken in the 60 day period beginning from the date of the notice. The Respondent should not file anything, as that would start the clock ticking all over again.

Motions to dismiss for failure to prosecute are governed by Florida Rule of Civil Procedure 1.420(e), the relevant parts of which states: "All actions in which it appears on the face of the record that no activity by filing of pleadings, order of court, or otherwise has occurred for a period of 1 year shall be dismissed by the court on its own motion or on the motion of any interested person, ... unless ... a party shows good cause ... why the action should remain pending. .... Mere inaction for a period of less than 1 year shall not be sufficient cause for dismissal for failure to prosecute. Therefore, a defendant looking to have a case dismissed would have to show there has been no record activity for the year preceding the motion. Second, if the defendant can succesfully show there has been no record activity, the plaintiff then has an opportunity to establish good cause why the action should not be dismissed. The one-year period in Rule 1.420(e) should be measured backwards from the time preceding the filing of the motion to dismiss for lack of prosecution. Florida courts have defined "record activity" as any act reflected in the court file that is designed to move the case forward toward a conclusion on the merits. So a simple administrative type order will not count as record activity.