If someone starts a divorce action and then changes their mind about it, then the consequences depend on the intentions of the other spouse. If the other spouse wants the divorce to proceed, then the divorce will proceed. But if the other spouse does NOT want the divorce, then the divorce action is dismissed, and the parties remain married.
As an example, if the husband commences the divorce action by serving a Petition, the wife has the option of serving an Answer and Counter-Petition, or just an Answer. By including the Counter-Petition, the wife is asserting that she wants the divorce to proceed whether the husband changes his mind or not. If the husband withdraws the Petition, then the divorce will proceed on the Counter-Petition. If the wife does not include a Counter-Petition, she is asserting that she does not want the divorce to proceed if the husband changes his mind and withdraws the Petition. In that instance, if the husband withdraws the Petition, there is no action on which to proceed.
If the parties decide to reconcile after the divorce begins, the parties must work together to withdraw the action. And of course, if they decide to reconcile after the divorce is final, then their options are to remarry, or to live happily ever after, together and unmarried.